Adam can wash and detail his car in 2 hours, and Lisa can wash and detail her car in 4 hours. If they work together, how long will it take them to wash and detail both cars?

Question

jamesj · Answer

The way to think about problems like this is in terms of $ \it rates $. 

The rate at which Michael can wash his car is
$$ R_M = 1/2 \ car/hour $$
In 1 hour, he washes 1/2 a car.

Lisa's rate is
$$ R_L = 1/4 $$

So far so good?

anonymous · Answer

yup :)

anonymous · Answer

so together they could do 3/4 of a car in 1 hour?

jamesj · Answer

Hence if they work together their combined rate is
$$ R = R_M + R_L $$ $$ = \frac{1}{2} + \frac{1}{4} = \frac{3}{4} $$

Therefore how long does it take them together to wash one car?

anonymous · Answer

so would it be 2 2/3 hours to wash both cars? lol i kinda think i skipped to the end

jamesj · Answer

To wash one car it takes 
$$ t = \frac{1 \ car}{ cars/hour} =  \frac{1}{3/4} = \frac{4}{3} \ hours $$

Hence two cars is 8/3 hours, which is what you wrote down.

It's worth however understanding this mathematics, because if you understand this once through and through, these problems will become trivial in the future.

anonymous · Answer

ahh ok i think i got it now..