## 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

1. Calcmathlete Group Title

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

2. Calcmathlete Group Title

So, if Jeff does the work in 2 hours, how much will he get done in 1 hour?

3. jrosesweet Group Title

the whole car?

4. Calcmathlete Group Title

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 Group Title

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 Group Title

so What equation is used to solve this problem? What does each variable represent?

7. jrosesweet Group Title

oh ok so thats the equation we use?

8. Calcmathlete Group Title

I just gave you the equation and the variable represents how long it takes for them to do it when they combine.

9. jrosesweet Group Title

oh thanks! so whats the solution?

10. jrosesweet Group Title

can i cross multiply to get the solution?

11. Calcmathlete Group Title

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 Group Title

so it would be the fraction of 6/7 ??

13. Calcmathlete Group Title

yup :)

14. jrosesweet Group Title

:) so thats the solution?

15. Calcmathlete Group Title

I believe so :)

16. jrosesweet Group Title

and last question, so how long does it take for BOTH of them to wash the car together?

17. Calcmathlete Group Title

18. jrosesweet Group Title

i plug in the solution and thats the time it takes for both of them...right

19. Calcmathlete Group Title

The solutions 6/7 is how long it takes to wash the car.

20. jrosesweet Group Title

but that doesnt make sense lol

21. Calcmathlete Group Title

@apoorvk Can you double check my work here?

22. Calcmathlete Group Title

I'm pretty sure that it would take 6/7 of an hour to wash the car together though...

23. jrosesweet Group Title

\OHH 6/7 of an hour. ok now it makes sense. thanks for all your help :)

24. Calcmathlete Group Title

np :)

25. apoorvk Group Title

@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 Group Title

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 Group Title

Work done in an hour is itself the rate - isn't it? ;)

28. Calcmathlete Group Title

lol...I have always been confused at this part...I'll take your word for it XD

29. apoorvk Group Title

No, don't take 'my' word - understand it and take your brain's word then ;)

30. Calcmathlete Group Title

Ok. $\frac 1x = \frac 76 = \text{Work rate}$

31. Calcmathlete Group Title

Than last question. What exactly would 6/7 be then?

32. apoorvk Group Title

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 Group Title

lol. no worries ;)

34. apoorvk Group Title

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