Question

Tom and Becky can paint Jim's fence together in $12$ hours. If all people paint at the same rate, how many hours would it take to paint the fence if Huck joins Tom and Becky, and all three of them paint Jim's fence together?

Answer 1

8 hours

Explanation

The first thing one mus realize here is that this is an inverse proportion question. When one quantity increases, the other decreases. That is the time needed to paint the fence decreases as the number of people who work on it increase. This means therefore that we can set up a proportionality equation:

`t \alpha (k)/(n)`

where t is time and n is the number of people. Given the information in the question we can find the proportionality constant k

`t=(k)/(n)`

`12=(k)/(2)`

so k=24

So how many hours does it take for 3 people

`t=(24)/(3) =8`