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jrosesweet Group Title

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?

  • 2 years ago
  • 2 years ago

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

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

    • 2 years ago
  3. jrosesweet Group Title
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    the whole car?

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

    • 2 years ago
  5. Calcmathlete Group Title
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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?

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

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

    • 2 years ago
  8. Calcmathlete Group Title
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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.

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

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

    • 2 years ago
  11. Calcmathlete Group Title
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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 = ?

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

    • 2 years ago
  13. Calcmathlete Group Title
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    yup :)

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

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

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

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

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

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

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

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

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

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

    • 2 years ago
  24. Calcmathlete Group Title
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    np :)

    • 2 years ago
  25. apoorvk Group Title
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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! :]

    • 2 years ago
  26. Calcmathlete Group Title
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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?

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

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

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

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

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

    • 2 years ago
  32. apoorvk Group Title
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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. -__-

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

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

    • 2 years ago
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