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jrosesweet

  • 2 years ago

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?

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  1. Calcmathlete
    • 2 years ago
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    Ok. First find how much work is done individually in one hour.

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

  3. jrosesweet
    • 2 years ago
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    the whole car?

  4. Calcmathlete
    • 2 years ago
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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, \(\frac12\).

  5. Calcmathlete
    • 2 years ago
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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?

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

  7. jrosesweet
    • 2 years ago
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    oh ok so thats the equation we use?

  8. Calcmathlete
    • 2 years ago
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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.

  9. jrosesweet
    • 2 years ago
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    oh thanks! so whats the solution?

  10. jrosesweet
    • 2 years ago
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    can i cross multiply to get the solution?

  11. Calcmathlete
    • 2 years ago
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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 = ?

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

  13. Calcmathlete
    • 2 years ago
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    yup :)

  14. jrosesweet
    • 2 years ago
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    :) so thats the solution?

  15. Calcmathlete
    • 2 years ago
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    I believe so :)

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

  17. Calcmathlete
    • 2 years ago
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    That's the answer...

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

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

  20. jrosesweet
    • 2 years ago
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    but that doesnt make sense lol

  21. Calcmathlete
    • 2 years ago
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    @apoorvk Can you double check my work here?

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

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

  24. Calcmathlete
    • 2 years ago
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    np :)

  25. apoorvk
    • 2 years ago
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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! :]

  26. Calcmathlete
    • 2 years ago
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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?

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

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

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

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

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

  32. apoorvk
    • 2 years ago
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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. -__-

  33. Calcmathlete
    • 2 years ago
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    lol. no worries ;)

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

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