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jrosesweet
 3 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?
jrosesweet
 3 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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Calcmathlete
 3 years ago
Best ResponseYou've already chosen the best response.2Ok. First find how much work is done individually in one hour.

Calcmathlete
 3 years ago
Best ResponseYou've already chosen the best response.2So, if Jeff does the work in 2 hours, how much will he get done in 1 hour?

Calcmathlete
 3 years ago
Best ResponseYou've already chosen the best response.2Well. 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, \(\frac12\).

Calcmathlete
 3 years ago
Best ResponseYou've already chosen the best response.2Now, 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?

jrosesweet
 3 years ago
Best ResponseYou've already chosen the best response.0so What equation is used to solve this problem? What does each variable represent?

jrosesweet
 3 years ago
Best ResponseYou've already chosen the best response.0oh ok so thats the equation we use?

Calcmathlete
 3 years ago
Best ResponseYou've already chosen the best response.2I just gave you the equation and the variable represents how long it takes for them to do it when they combine.

jrosesweet
 3 years ago
Best ResponseYou've already chosen the best response.0oh thanks! so whats the solution?

jrosesweet
 3 years ago
Best ResponseYou've already chosen the best response.0can i cross multiply to get the solution?

Calcmathlete
 3 years ago
Best ResponseYou've already chosen the best response.2I 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 = ?

jrosesweet
 3 years ago
Best ResponseYou've already chosen the best response.0so it would be the fraction of 6/7 ??

jrosesweet
 3 years ago
Best ResponseYou've already chosen the best response.0:) so thats the solution?

jrosesweet
 3 years ago
Best ResponseYou've already chosen the best response.0and last question, so how long does it take for BOTH of them to wash the car together?

Calcmathlete
 3 years ago
Best ResponseYou've already chosen the best response.2That's the answer...

jrosesweet
 3 years ago
Best ResponseYou've already chosen the best response.0i plug in the solution and thats the time it takes for both of them...right

Calcmathlete
 3 years ago
Best ResponseYou've already chosen the best response.2The solutions 6/7 is how long it takes to wash the car.

jrosesweet
 3 years ago
Best ResponseYou've already chosen the best response.0but that doesnt make sense lol

Calcmathlete
 3 years ago
Best ResponseYou've already chosen the best response.2@apoorvk Can you double check my work here?

Calcmathlete
 3 years ago
Best ResponseYou've already chosen the best response.2I'm pretty sure that it would take 6/7 of an hour to wash the car together though...

jrosesweet
 3 years ago
Best ResponseYou've already chosen the best response.0\OHH 6/7 of an hour. ok now it makes sense. thanks for all your help :)

apoorvk
 3 years ago
Best ResponseYou've already chosen the best response.1@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! :]

Calcmathlete
 3 years ago
Best ResponseYou've already chosen the best response.2Oh 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?

apoorvk
 3 years ago
Best ResponseYou've already chosen the best response.1Work done in an hour is itself the rate  isn't it? ;)

Calcmathlete
 3 years ago
Best ResponseYou've already chosen the best response.2lol...I have always been confused at this part...I'll take your word for it XD

apoorvk
 3 years ago
Best ResponseYou've already chosen the best response.1No, don't take 'my' word  understand it and take your brain's word then ;)

Calcmathlete
 3 years ago
Best ResponseYou've already chosen the best response.2Ok. \[\frac 1x = \frac 76 = \text{Work rate}\]\[\]

Calcmathlete
 3 years ago
Best ResponseYou've already chosen the best response.2Than last question. What exactly would 6/7 be then?

apoorvk
 3 years ago
Best ResponseYou've already chosen the best response.1Oh wait  itismy 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. __

Calcmathlete
 3 years ago
Best ResponseYou've already chosen the best response.2lol. no worries ;)

apoorvk
 3 years ago
Best ResponseYou've already chosen the best response.1I thought *1/2 + 1/1.5* was 6/7  so I made that mixup. Apologies once again!
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