Question

As a punishment for something naughty that we did, my little brother and I have to whitewash both sides of a fence. We start at the same time, and we each work at a constant rate.

If we each whitewash one side, I'll finish in 2 hours and my brother will finish in 3
hours. But I'm a nice kid, so after I finish my side, I go around to the other side and help my brother finish his side. From the time I start helping him, how many minutes does it take us to finish the job?

Answer 1

@mathmate

Answer 2

can yall help

Answer 3

@mayankdevnani

Answer 4

In this problem doing the job means whitewashing one side of the fence.
If you do the job in 2 hours, what part of the job will you do in 1 hour?

Answer 5

The job is x

Part of job done in 1 hour
You Your brother Working together
x/2 x/3 x/2 + x/3 =3x/6 + 2x/6 = 5x/6

You do your side in 2 hours.
Your brother is doing his side which will take 3 hours.
After you finish your side, he has done 2 hours of 3 hours to do his side.
That means he has done 2/3 of the job, and only 1/3 of the job is left to do.

Now you must do 1/3 of the job, or x/3, and the two of you working together
do 5x/6 in an hour.