Daria can wash and detail 3 cars in 2 hours. Larry can wash and detail the same 3 cars in 1.5 hours. About how long will it take to wash and detail the 3 cars Daria and Larry worked together?

Question

anonymous · Answer

I was wondering what they mean by put differently? why is it 1/3.5 and not 3.5 over 1?
Someone responded earlier:
hickninja
So Daria washes 1.5 cars per hour, and Larry washes 2 cars per hour. Assuming they work together perfectly, they can wash 3.5 cars per hour. Put differently, together they wash 1/3.5 = 2/7 cars per hour. So to wash 3 cars, it will take 3 * 2/7 = 6/7 of an hour. This works out to be about 51 minutes. 6/7 hr * 60 min/hr = 51 min.

richyw · Answer

$$\frac{3cars}{2hours}+\frac{3cars}{1.5hours}=\frac{9cars}{2hours}$$
$$\frac{3 cars}{\frac{9cars}{2hours}}=6/9=2/3=40 mins$$

richyw · Answer

not sure if those fractions are correct at all. I'm tired

anonymous · Answer

It's multiple choice, and the correct answer is 51, so it must make some kind of sense

richyw · Answer

hmm give me a second i'll see what I did wrong

anonymous · Answer

take your time!! :)

richyw · Answer

oops ok that first fraction should be $$\frac{7}{2}$$ then $$\frac{3}{\frac{7}{2}}=\frac{6}{7}$$ which is 51.4mins

richyw · Answer

so yeah, add the two rates and then divide the number of cars by the combined rate...

richyw · Answer

of course you can just take the shortcut since they are both the same number of cars in the initial problem and just do 3/3.5

richyw · Answer

but the way I showed will work even if the initial rate was like "2 cars in 4 hours" and "5 cars in 2" hours

anonymous · Answer

hmm, this is calc free so it takes me a while

richyw · Answer

I know what you mean. It's always the the simple stuff like this that messes me up

anonymous · Answer

add the two rates (cars per hour) which equal 3.5cars/1hr combined. And then divide the number of cars(3) by the combined rate (cars per hr). instead of multiplying the reversed fraction she had, divide the cars per hr. Your ending makes more sense to me.  
$$1.5car/hr + 2car/hr = 7cars/2 hr$$
and 3cars made at that rate takes 6/7hr. all better! thanks man