Question

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?

Answer 1

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

Answer 2

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

Answer 3

the whole car?

Answer 4

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, \(\frac12\).

Answer 5

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?

Answer 6

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

Answer 7

oh ok so thats the equation we use?

Answer 8

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

Answer 9

oh thanks! so whats the solution?

Answer 10

can i cross multiply to get the solution?

Answer 11

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 = ?

Answer 12

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

Answer 13

yup :)

Answer 14

:) so thats the solution?

Answer 15

I believe so :)

Answer 16

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

Answer 17

That's the answer...

Answer 18

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

Answer 19

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

Answer 20

but that doesnt make sense lol

Answer 21

@apoorvk Can you double check my work here?

Answer 22

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

Answer 23

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

Answer 24

np :)

Answer 25

@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! :]

Answer 26

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?

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

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

Answer 31

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

Answer 32

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. -__-

Answer 33

lol. no worries ;)

Answer 34

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