Greener Group Title 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? 2 years ago 2 years ago

1. Greener Group Title

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.

2. richyw Group Title

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

3. richyw Group Title

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

4. Greener Group Title

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

5. richyw Group Title

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

6. Greener Group Title

7. richyw Group Title

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

8. richyw Group Title

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

9. richyw Group Title

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

10. richyw Group Title

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

11. Greener Group Title

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

12. richyw Group Title

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

13. Greener Group Title

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