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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?

Mathematics
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Ok. First find how much work is done individually in one hour.
So, if Jeff does the work in 2 hours, how much will he get done in 1 hour?
the whole car?

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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, \(\frac12\).
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?
so What equation is used to solve this problem? What does each variable represent?
oh ok so thats the equation we use?
I just gave you the equation and the variable represents how long it takes for them to do it when they combine.
oh thanks! so whats the solution?
can i cross multiply to get the solution?
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 = ?
so it would be the fraction of 6/7 ??
yup :)
:) so thats the solution?
I believe so :)
and last question, so how long does it take for BOTH of them to wash the car together?
That's the answer...
i plug in the solution and thats the time it takes for both of them...right
The solutions 6/7 is how long it takes to wash the car.
but that doesnt make sense lol
@apoorvk Can you double check my work here?
I'm pretty sure that it would take 6/7 of an hour to wash the car together though...
\OHH 6/7 of an hour. ok now it makes sense. thanks for all your help :)
np :)
@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! :]
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?
Work done in an hour is itself the rate - isn't it? ;)
lol...I have always been confused at this part...I'll take your word for it XD
No, don't take 'my' word - understand it and take your brain's word then ;)
Ok. \[\frac 1x = \frac 76 = \text{Work rate}\]\[\]
Than last question. What exactly would 6/7 be then?
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. -__-
lol. no worries ;)
I thought *1/2 + 1/1.5* was 6/7 - so I made that mix-up. Apologies once again!

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