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

4 hours & 30 minutes?

Answer 2

So this is a question that can be worked on as an equation.

You work faster than your brother and we have to figure out how much faster first. Where your brother takes 3 hours, you take 2. So you work at a rate of 3/2 times faster than your brother. Or, for every 2 parts your brother covers, you cover three.

Now imagine you have completed your side of the fence. Your brother will still have an hour of work to go. But if you split it such that you both finish at the same time, you should take a bit more since you work faster. So if we split it at the ratio of 3:2, it means your brother gets 24 minutes of work and you get 36 minutes of his work. Remember we are splitting according to his work rate.