Rational Expressions Word Problems: Work Rate Problems

www.greenemath.com/
In this video, we explain how to setup and solve a "work rate" problem. This type of problem is also referred to as a "rate of work problem". These problems are pretty easy to solve. We just find out how much each person contributes per unit of time. We then sum each contribution, to find out the total contribution per unit of time. After this we setup an equation to find out how many units of time are needed.

Пікірлер: 135

  • @katemarsh8799
    @katemarsh87993 жыл бұрын

    8 years ago and he still replies to the comments, salute🙋🏻‍♀️

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    Got nothing better to do after work 😂

  • @FuzedToons

    @FuzedToons

    2 жыл бұрын

    ikr

  • @letanxuong3953

    @letanxuong3953

    14 күн бұрын

    ​@@Greenemathare there videos organized into playlists for statistics at college level?

  • @b07-gabrielchristophers.85
    @b07-gabrielchristophers.854 жыл бұрын

    dude youre so underrated i appreciate it so much

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    You are very welcome! :)

  • @ackoonsgaming
    @ackoonsgaming Жыл бұрын

    God Bless You. This was exactly what I need for my test tomorrow.

  • @Greenemath

    @Greenemath

    Жыл бұрын

    Awesome, good luck!

  • @bandini22221
    @bandini222212 жыл бұрын

    thank you. It's been many years since I've done this stuff.

  • @Greenemath

    @Greenemath

    2 жыл бұрын

    You are very welcome.

  • @rjheldereal7866
    @rjheldereal78662 жыл бұрын

    We can handle these applications involving work in a manner similar to the method we used to solve distance, speed, and time problems. Work = Rate x Time. Suppose you can finish a report in 2 hours. Your classmate can finish the same report in 4 hours. How long will it take to finish the report if both of you work together?

  • @Greenemath

    @Greenemath

    2 жыл бұрын

    Yes the strategy is the same, but since it is set equal to one completed job, you can solve the problem by just finding the reciprocal.

  • @roaabetar4019
    @roaabetar40193 жыл бұрын

    Hi, thank you for helping. Do you have more videos of solving rational expression word problems? if yes could you please just post the link here in a comment for me, I would appreciate it!

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    kzread.info/dash/bejne/q4KL2c9udLCvmrw.html

  • @FuzedToons
    @FuzedToons2 жыл бұрын

    Thanks for your explanation, it helped me a lot in my video assignment!

  • @Greenemath

    @Greenemath

    2 жыл бұрын

    Glad it helped!

  • @trishydaley
    @trishydaley3 жыл бұрын

    Thank you so much you helped me a lot with my homework that my teacher didn't even discuss😩

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    You're very welcome!

  • @saitokensuzuki5058
    @saitokensuzuki50584 жыл бұрын

    Ty dude it really helped me in my exam

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    Perfect, glad it helped :)

  • @hi-il7ug
    @hi-il7ug2 жыл бұрын

    can’t believe this video was uploaded when I was 5. watching this 9 years later, struggling in alg2.

  • @Greenemath

    @Greenemath

    2 жыл бұрын

    Time really does fly! Good luck with your class.

  • @jochebedrequiez5458
    @jochebedrequiez54582 жыл бұрын

    hello! I was wonderinf what kind of rational expression this was? Is it a rational function, rational equality, or rational inequality?

  • @Greenemath

    @Greenemath

    2 жыл бұрын

    For a work rate problem, in most cases, you would end up setting up a rational equation.

  • @adriannavictorina6739
    @adriannavictorina67392 жыл бұрын

    thank u for this, this really help me in my math

  • @Greenemath

    @Greenemath

    2 жыл бұрын

    Glad it helped!

  • @wpxxfighting3837
    @wpxxfighting38373 жыл бұрын

    In a car wash station, Dave, Ernie and Frank can was and vacuum the interior of a car in 3 hours, 1 1/2 hours and 2 hours respectively when working alone. How long will it take to wash the car and vacuum its interior if Dave and Ernie work together?

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    Just to be clear, it's just Dave and Ernie working together? This means that Frank is irrelevant or did you make a typo? Since Dave can do the job in 3 hours, in 1 hour, he does 1/3 of the job. Sine Ernie can do the job in 1.5 hours, in 1 hour he does 2/3 of the job. Note that 1 1/2 hours is 1.5 or 3/2. You would need to do 1/1.5 or 1/(3/2) So in 1 hour how much can they do together? 1/3 + 2/3 = 1 This one is really easy since it's obvious that it takes them 1 hour when working together. Let me know if you have another question.

  • @wpxxfighting3837

    @wpxxfighting3837

    3 жыл бұрын

    This is late but thank you❤️@@Greenemath

  • @millieo3045
    @millieo30453 жыл бұрын

    thank you so much!!!! this really helped me

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    I'm so glad!

  • @shift4910
    @shift4910 Жыл бұрын

    Can someone help me if it takes angelo 10 minutes at the rate of 1/20 of the easy assignment per minute then he does 10/20 or 1/2 of the assignments that each boy does is a fraction of the whole work. so the expressions for school work in the last column of the table have a sum of 1

  • @Greenemath

    @Greenemath

    Жыл бұрын

    Did you get it yet?

  • @utkarma8132
    @utkarma81322 жыл бұрын

    ur good at explaining stuff lol and u responded to most comments sheesh

  • @Greenemath

    @Greenemath

    2 жыл бұрын

    I only get like 3 comments a day so it's pretty easy. Good luck with class.

  • @Miyukiyo
    @Miyukiyo Жыл бұрын

    Is 4 4/17 hours a correct answer for this too?

  • @Greenemath

    @Greenemath

    Жыл бұрын

    The correct answer for what exactly? If you leave a time marker I can check for you.

  • @th3qsfr
    @th3qsfr2 жыл бұрын

    Thank you! This helps me

  • @Greenemath

    @Greenemath

    2 жыл бұрын

    Glad it helped!

  • @clapyourfeetandclapyourhan5441
    @clapyourfeetandclapyourhan54412 жыл бұрын

    Thank you for this. It's my math exam tomorrow.

  • @Greenemath

    @Greenemath

    2 жыл бұрын

    Best of luck!

  • @esmarlynjaquez2612
    @esmarlynjaquez2612Ай бұрын

    YOU ARE AMAZING!!!

  • @Greenemath

    @Greenemath

    Ай бұрын

    Thanks, I appreciate the nice comment.

  • @liaminabox9651
    @liaminabox96512 жыл бұрын

    Damn this is a great tutorial thanks

  • @Greenemath

    @Greenemath

    2 жыл бұрын

    You are welcome!

  • @cameloogabooga
    @cameloogabooga Жыл бұрын

    Thank you 🙏🙏 I have a test tomorrow

  • @Greenemath

    @Greenemath

    Жыл бұрын

    Best of luck!

  • @kenshibual3091
    @kenshibual30913 жыл бұрын

    This is very helpful✌️

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    Glad to hear that!

  • @Tywild327
    @Tywild327 Жыл бұрын

    How do I do subtracting?

  • @Greenemath

    @Greenemath

    Жыл бұрын

    What's the problem you are stuck on?

  • @lebronemichael5697
    @lebronemichael56973 жыл бұрын

    Working Alone,Carlos can oil the lanes in a bowling alley in five hours.jenny can oil the same lanes in nie hours.if they work together how long it would take them?

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    Just break things down into 1 unit of time. We are working in terms of hours. So Carlos can oil the lanes in 5 hours. How much of this can he do in 1 hour? 1 hour -> 1/5 of the job Now for Jenny, she takes longer, it takes her 9 hours. How much of this can she do in 1 hour? 1 hour -> 1/9 of the job Now if they work together for 1 hour how much of the job will they complete? 1/5 + 1/9 = 14/45 Now we can set up a simple equation where x is the number of hours to complete 1 job. (14/45)x = 1 x = 45/14 or about 3.21 hours

  • @lebronemichael5697

    @lebronemichael5697

    3 жыл бұрын

    Working alone,it takes kristin 11 hours to harvest field.kayla can harvest the same field in 16 hours.find how long it would take them if they worked together?

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    @@lebronemichael5697 It's the same set up, how much is done in 1 hour by Kristin plus how much is done in one unit of time by Kayla 1/11 + 1/16 = 27/176 So this is the amount they do in 1 hour together. If x is the time in hours to complete 1 job: (27/176)x = 1 x is 176/27 or about 6.52 hours

  • @lebronemichael5697

    @lebronemichael5697

    3 жыл бұрын

    Thankyou bro you're an angel😌❤️

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    @@lebronemichael5697 You are welcome, I hope you understand the concept and can pass your test :)

  • @ayeee1095
    @ayeee10952 жыл бұрын

    yay, i have an example now cuz were needed to make one.. thx u

  • @Greenemath

    @Greenemath

    2 жыл бұрын

    You are welcome!

  • @charyzduran3538
    @charyzduran35383 жыл бұрын

    An experienced roofer can a roof a house in 26 hrs. A beginner needs a 39 hrs to do the same job. How long it will take if they work together?

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    These are sooo easy. The first guy does 1/26 worth of the job in an hour and the second guy does 1/39 worth of the job in an hour. If they work together, how much of the job is completed in 1 hour? 1/26 + 1/39 = 5/78 So this is the amount completed by both of these guys in 1 hour. So then if we let x be equal to the amount of hours it takes to complete 1 job: (5/78)x = 1 x = 78/5 So it would take 15.6 hours to complete the job if they both work together.

  • @charyzduran3538

    @charyzduran3538

    3 жыл бұрын

    @@Greenemath thank you💜💜

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    @@charyzduran3538 You are very welcome, let me know if you get stuck on another problem :)

  • @dr.manikdhawan5725
    @dr.manikdhawan57253 жыл бұрын

    A large auger can fill a grain bin in 5 h less time than a smaller auger. Together they fill the bin in 6 h. How long would it take the larger auger, by itself, to fill the bin?

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    Did you get this?

  • @dr.manikdhawan5725

    @dr.manikdhawan5725

    3 жыл бұрын

    @@Greenemath I am sorry I used this method by it didn't work, i really appreciate you replying. Can you please explain?

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    @@dr.manikdhawan5725 Yes, when I get off work in a few hours, I'll write out a solution for you.

  • @dr.manikdhawan5725

    @dr.manikdhawan5725

    3 жыл бұрын

    @@Greenemath thanks very much!!

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    @@dr.manikdhawan5725 To start out the problem, you would want to set something up like this: let x = time in hours for the small auger then x - 5 = time in hours for the larger auger (since it takes 5 hours less time we subtract 5 away from x) For these problems, the first thing you want to do is think about what is accomplished in 1 unit of time. In 1 hour: Small Auger: 1/x of the job is done Large Auger: 1/(x - 5) of the job is done Let's add these two fractions to get the total amount done in 1 hour if they work together. 1/x + 1/(x - 5) = (2x - 5)/(x(x - 5)) Now, we are told in the problem that working together they accomplish the job in 6 hours. This means we can multiply our fraction by 6 and set this equal to 1 (1 complete job) (2x - 5)/(x (x - 5)) * 6 = 1 Simplify: (12x - 30)/(x(x - 5)) = 1 Now, we want to solve the equation for x, this will give us the time it takes in hours for the small auger to complete the job. Since you want the time for the large auger, we can just subtract 5 from this result. (12x - 30)/(x(x - 5)) = 1 (12x - 30)/(x^2 - 5x) = 1 12x - 30 = x^2 - 5x x^2 -17x + 30 = 0 (x - 15)(x - 2) = 0 x = 15, 2 Since we multiplied both sides by a variable expression, we got an extraneous solution. x = 2 does not work, but x = 15 does. This tells us that the large auger can do the job in 10 hours (15 - 5). You can check this: In 1 hour the large auger does (1/10) of the job and the small auger does (1/15) of the job. Multiply these by 6 since it takes 6 hours working together to complete the job and we should get 1 if we are correct. (1/10) * 6 + (1/15) * 6 = 1 6/10 + 6/15 = 1 3/5 + 2/5 = 1 5/5 = 1 1 = 1 So our solution is correct, it takes the large auger 10 hours to complete the job.

  • @dreig8305
    @dreig83053 жыл бұрын

    thanks it's perfect

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    You're welcome!

  • @harukawashinobu5928
    @harukawashinobu5928 Жыл бұрын

    Thank you very much

  • @Greenemath

    @Greenemath

    Жыл бұрын

    You are welcome

  • @chloekim3548
    @chloekim35483 жыл бұрын

    It takes 10 hours to fill a pool using the inlet pipe. It can be drained in 15 hours using the outlet pipe. If the pool is half full, how long will it take to fill it if both pipes are open?

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    For this problem, you have two competing forces. One is filling up the pool and the other is draining the pool. Let's start by just thinking about the pool being completely empty and then we will address the 1/2 full part. It takes 10 hours to fill the pool so in 1 hour 1/10 of the job is done It takes 15 hours to drain the pool so in 1 hour 1/15 of the job is done Let's subtract: 1/10 - 1/15 = 1/30 So this means the pool would be 1/30 filled in 1 hour with the two competing forces. If the pool was completely empty, this means it would take 30 hours to complete the job. (1/30)x = 1 x = 30 In your case, you only need to complete half of the job, because the pool is half full. So logically it will only take 15 hours. (1/30)x = 1/2 x = 15

  • @chloekim3548

    @chloekim3548

    3 жыл бұрын

    @@Greenemath THANNKYYYOU SM.♥️

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    @@chloekim3548 You are welcome! :)

  • @chloekim3548

    @chloekim3548

    3 жыл бұрын

    @@Greenemath can i ask one more? Hehe 😅 Vhong from his home, jogs a certain distance at a rate of 8 kilometers per hour. He runs back home over the same track at the rate of 24 kilometers per hour. If it took him 2 hours and 30 minutes jogging and running, what is the total distance travelled?

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    @@chloekim3548 Hi, you are watching a work/rate video, this is a motion word problem. You can think about it this way: distance (d) = rate of speed (r) x time traveled (t) In this case, you are given the rate of speed for jogging (8 kilometers per hour) and running (24 kilometers per hour). You are not given individual times, but a combined time of 2.5 hours. let x = time spent jogging in hours, then 2.5 - x = time spent running Now we know that d = r x t d1 = 8x d2 = 24(2.5 - x) Where d1 is from jogging and d2 is from running. We know that the distances are equal since he jogs to some place and runs back over the same track. This means we can set the two equal to each other. 8x = 24(2.5 - x) 8x = 60 - 24x 32x = 60 x = 15/8 = 1.875 Now the problem asks for the total distance traveled, so let's plug into d1 and d2 from above: d1 = 8(15/8) d2 = 24(2.5 - 1.875) d1 = 15 d2 = 15 This should make sense as the distance there and the distance back is the same, the only difference is the amount of time it takes. So the total distance traveled is the sum of the two: d1 + d2 = 15 + 15 = 30. This means Vhong travled 30 kilometers.

  • @azaleafernandez4703
    @azaleafernandez47033 жыл бұрын

    A printing machine can run the necessary copies of the daily circulation of a newspaper in 8 hours. A modern printer can run the same number of copies in 5 hours. How long will it take to run the copies when both machines are working?

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    So just think about the amount of the job that can be done in 1 unit of time. Here, we are working with hours: printing machine 1 hour : 1/8 of the job modern printer 1 hour: 1/5 of the job So if we combine theses two amounts through addition, we will see how much of the job that is done in 1 unit of time by both machines: 1/8 + 1/5 = 13/40 Now we know that in 1 hour 13/40 of the job is completed with the two machines working together. (13/40)x = 1 let x be the number of hours required to complete one job. x = 40/13 hours or about 3.08 hours if you approximate.

  • @azaleafernandez4703

    @azaleafernandez4703

    3 жыл бұрын

    @@Greenemath Thank youu

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    @@azaleafernandez4703 You are welcome :)

  • @ldknk
    @ldknk Жыл бұрын

    Thank u!

  • @Greenemath

    @Greenemath

    Жыл бұрын

    You're welcome!

  • @hounddoggurxi203
    @hounddoggurxi2032 жыл бұрын

    How to be good at math if you are completely left behind from basic to intermediate math?

  • @Greenemath

    @Greenemath

    2 жыл бұрын

    To be good at math you need to work lots and lots of practice problems. Videos on youtube can just show you the steps, but you need to work problems to be good at math. Just like watching someone play golf will not help you get any better, watching someone else do math won't be that much help.

  • @hughjanuz4343
    @hughjanuz4343 Жыл бұрын

    He put a lot of explanation there but the equation's just: 1/1st person rate + 1/2nd person rate + etc. = 1/x, after you add the fraction, cross multiply to 1/x or just use the reciprocal of the fraction you add

  • @Greenemath

    @Greenemath

    Жыл бұрын

    Just depends on the problem type. For simpler problems such as in this video, what you describe is the set up but in some cases, you may need to do a bit more to obtain your solution.

  • @hughjanuz4343

    @hughjanuz4343

    Жыл бұрын

    @@Greenemath ohh didn't know that, thanks! 😁

  • @alenalovess379
    @alenalovess3792 жыл бұрын

    Thankss for thiss😊😊

  • @Greenemath

    @Greenemath

    2 жыл бұрын

    Welcome 😊

  • @sinashrose8290
    @sinashrose8290 Жыл бұрын

    10 years ago!!!! :O

  • @Greenemath

    @Greenemath

    Жыл бұрын

    Yes!

  • @4gbrown4
    @4gbrown410 жыл бұрын

    This video makes this process a lot more complicated than it has to be. YOUR COMPLICATING THINGS.

  • @b07-gabrielchristophers.85

    @b07-gabrielchristophers.85

    4 жыл бұрын

    silence liberal

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    I'm sorry you feel that way, the process is quite simple.

  • @4gbrown4

    @4gbrown4

    3 жыл бұрын

    6 years ago. I don’t even remember what the video was about.

  • @4gbrown4

    @4gbrown4

    3 жыл бұрын

    @@b07-gabrielchristophers.85 shut your mouth you ignorant sod.

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    @@4gbrown4 It's cool, I was answering another comment and saw one that I missed. Hope all is well :)

  • @GenghisDom
    @GenghisDom3 жыл бұрын

    As someone from the upper midwest I found the southern pronunciation of "oil" very distracting, good video though. My college algebra professor has hardly taught us anything this year.

  • @shakiramaetorres482
    @shakiramaetorres4829 ай бұрын

    im your new subscriber

  • @Greenemath

    @Greenemath

    9 ай бұрын

    Welcome, I hope you find the channel helpful!

  • @Sinistermk.
    @Sinistermk.2 жыл бұрын

    I have been stuck here for a week know rewatching your vid trying to understand it this problem i think is not a work rate problem but still a word problem The denominator of a certain number is 2 more than The numerator. When both numerator and denominator is increased by 3 the fraction will be 23. What is the original fraction (x/+2) =(x+3/+2+3) = 23 what is the original fraction?

  • @Sinistermk.

    @Sinistermk.

    2 жыл бұрын

    I hope u can help me :)

  • @Greenemath

    @Greenemath

    2 жыл бұрын

    This is not a work rate problem. Why would you re-watch this video when you know it has nothing to do with the set up of your word problem? Are you sure you typed that correctly. The grammar seems way off. (x) / (x + 2) -> original fraction But it says certain number, not fraction which isn't typical of a word problem. (x + 3) / (x + 5) = 23 But it says the fraction will be 23, this is a whole number. If you solve for x: x + 3 = 23(x + 5) x + 3 = 23x + 115 -22x = 112 x = -56/11 This is not the answer, you would need to plug back in: (x) / (x + 2) -> original fraction (-56/11) / (-56/11 + 2) ---------------------------------------- Check one: It says if we increase both numerator (-56/11) and denominator (-34/11) by 3, the fraction will be 23: (-56/11) / (-34/11) (-56/11 + 3) / (-34/11 + 3) = 23 (-23/11) / (-1/11) = 23 23 = 23 True Check two: It says the denominator is 2 more than the numerator: (-56/11 + 2) = -34/11 -34/11 = -34/11 True So your number as this problem is written is the complex fraction (-56/11) / (-34/11), which simplifies to 28/17. I think you wrote the problem incorrectly, but if it is correct it's a really sloppy problem.

  • @cloudfone1885
    @cloudfone18853 жыл бұрын

    If I work 15 hours and you work 30 hours,how will I get the answer??

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    If it takes you 15 hours to do the job and me 30 hours to do the job, then in one hour you have done 1/15 of the job and I have done 1/30 of the job. So we can combine those amounts: 1/15 + 1/30 = 3/30 = 1/10. So this means together, we have accomplished 1/10 of the job in one hour, so it would take 10 hours for us to do the job working together. :)

  • @lava-chanyt9176
    @lava-chanyt91763 жыл бұрын

    If I work 1 hour and 30 minutes, and you 2 hour's, how will it take if we both work together?

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    That can't be your problem, you need more information. Is the problem saying that one person completes the job in 1 hour and 30 minutes and the other in 2 hours? In this case, convert each to minutes or to hours, just pick one. So 1 hour and 30 minutes is 90 minutes, 2 hours is 120 minutes. Person 1 in 1 minute does 1/90 of the job Person 2 in 1 minute does 1/120 of the job How much do they do together in 1 minute? 1/90 + 1/120 = 7/360 7/360 x = 1 So how much is completed in 1 minute times the number of minutes to complete the job gives us 1 complete job. x = 360/7 which is about 51.43 minutes This means if the two people work together, the job will be completed in about 51.43 minutes.

  • @lava-chanyt9176

    @lava-chanyt9176

    3 жыл бұрын

    @@Greenemath OH MAN- OMG THANK YOU!!!! now I can answer my quizಥ‿ಥ💜 thank you thank you thank youuuuuuuuuu

  • @xyrillabinasa312
    @xyrillabinasa3122 жыл бұрын

    I appreciate it, it is informational but I think it will be better if you could focus more on explaining than making sentences. Please avoid explaining too much of the same thing again and again. That's all thank you.

  • @Greenemath

    @Greenemath

    2 жыл бұрын

    For you I explained too much, for others I didn't explain enough. This is why I rarely make math videos anymore! Thanks for watching and good luck with your studies.

  • @gidxxeawwrrr6099
    @gidxxeawwrrr60993 жыл бұрын

    How to make problems? Ask math

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    😎

  • @armaandrar4087
    @armaandrar40873 жыл бұрын

    Hi

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    Are you a bot? I can't tell, there are soo many bots on KZread.

  • @Nitro-wg6sr

    @Nitro-wg6sr

    3 жыл бұрын

    @@Greenemath most likely a bot or a small child

  • @Greenemath

    @Greenemath

    3 жыл бұрын

    @@Nitro-wg6sr It's a bot, half of KZread is bots with those dumb links... 🙄