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jrosesweet

PLEASE HELP, EASY Jeff and Lucy have been asked to wash their mom’s minivan. It takes Jeff 2 hours to wash the van by himself, and it takes Lucy 1.5 hours to wash the van by herself. How long will it take Jeff and Lucy to wash the van if they work together?

  • one year ago
  • one year ago

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  1. Calcmathlete
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    Ok. First find how much work is done individually in one hour.

    • one year ago
  2. Calcmathlete
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    So, if Jeff does the work in 2 hours, how much will he get done in 1 hour?

    • one year ago
  3. jrosesweet
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    the whole car?

    • one year ago
  4. Calcmathlete
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    Well. In 2 hours, he gets all of the work done. In 1 hour, he gets half the work done because it's half the time it takes. Does that make sense? In other words, \(\frac12\).

    • one year ago
  5. Calcmathlete
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    Now, in one hour, Lucy does \(\LARGE \frac{1}{1.5}\) amount of the work. If you combine it, you get this. \[\huge\frac 12 + \frac{1}{1.5} = \frac1x\]Can you solve for x here?

    • one year ago
  6. jrosesweet
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    so What equation is used to solve this problem? What does each variable represent?

    • one year ago
  7. jrosesweet
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    oh ok so thats the equation we use?

    • one year ago
  8. Calcmathlete
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    I just gave you the equation and the variable represents how long it takes for them to do it when they combine.

    • one year ago
  9. jrosesweet
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    oh thanks! so whats the solution?

    • one year ago
  10. jrosesweet
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    can i cross multiply to get the solution?

    • one year ago
  11. Calcmathlete
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    I suppose you can, but you have to in the very least get a common denominator before that. \[\frac 12 \times \frac33+ \frac{1}{1.5} \times\frac44= \frac 1x \implies \frac 36 + \frac46 = \frac1x \implies \frac{7}{6} = \frac1x\]Now you can cross multiply. 7x = 6 x = ?

    • one year ago
  12. jrosesweet
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    so it would be the fraction of 6/7 ??

    • one year ago
  13. Calcmathlete
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    yup :)

    • one year ago
  14. jrosesweet
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    :) so thats the solution?

    • one year ago
  15. Calcmathlete
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    I believe so :)

    • one year ago
  16. jrosesweet
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    and last question, so how long does it take for BOTH of them to wash the car together?

    • one year ago
  17. Calcmathlete
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    That's the answer...

    • one year ago
  18. jrosesweet
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    i plug in the solution and thats the time it takes for both of them...right

    • one year ago
  19. Calcmathlete
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    The solutions 6/7 is how long it takes to wash the car.

    • one year ago
  20. jrosesweet
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    but that doesnt make sense lol

    • one year ago
  21. Calcmathlete
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    @apoorvk Can you double check my work here?

    • one year ago
  22. Calcmathlete
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    I'm pretty sure that it would take 6/7 of an hour to wash the car together though...

    • one year ago
  23. jrosesweet
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    \OHH 6/7 of an hour. ok now it makes sense. thanks for all your help :)

    • one year ago
  24. Calcmathlete
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    np :)

    • one year ago
  25. apoorvk
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    @Calcmathlete yeah you are right - well almost. :P Actually 1/2 + 1/(1.5) gives you the work that can be completed by both kids together *in an hour* - so they basically complete 6/7 of the work in an hour. Hence they will need 1/(6/7), i.e. 7/6 hours to complete the work from scratch! :]

    • one year ago
  26. Calcmathlete
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    Oh ok. I was always under the impressions that since \(\LARGE \frac 1x\) represents work done in an hour, the reciprocal which is x would give you the combined rate?

    • one year ago
  27. apoorvk
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    Work done in an hour is itself the rate - isn't it? ;)

    • one year ago
  28. Calcmathlete
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    lol...I have always been confused at this part...I'll take your word for it XD

    • one year ago
  29. apoorvk
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    No, don't take 'my' word - understand it and take your brain's word then ;)

    • one year ago
  30. Calcmathlete
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    Ok. \[\frac 1x = \frac 76 = \text{Work rate}\]\[\]

    • one year ago
  31. Calcmathlete
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    Than last question. What exactly would 6/7 be then?

    • one year ago
  32. apoorvk
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    Oh wait - it-is-my bad! :O I completely misread what you'd written! ಠ_ಠ You had got 1/2 + 1/1.5 = 7/6, and so ofcourse the complete the work in 6/7 hours together!! I am really sorry, am stupid. -__-

    • one year ago
  33. Calcmathlete
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    lol. no worries ;)

    • one year ago
  34. apoorvk
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    I thought *1/2 + 1/1.5* was 6/7 - so I made that mix-up. Apologies once again!

    • one year ago
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