Question

A carpenter can build a toolshed three times as fast as his apprentice. Working together,
they can build the shed in 6 hours. How long would it take each of them working alone to build the shed?

Answer 1

Let the time taken by the carpenter to build the tool shed, working alone, be x hours.
Then the apprentice, working alone, will take 3x hours.
Working alone, the carpenter will complete 1/x of the tool shed in one hour and the apprentice will complete 1/(3x) of the tool shed in one hour.
Working together they will complete 1/6 of the tool shed in one one hour.
Therefore we can write the equation:
\[\large \frac{1}{x}+\frac{1}{3x}=\frac{1}{6}\ .........(1)\]
Simplifying equation (1) gives:
\[\large 3x=24\]
which gives x = 8.
Therefore it takes the carpenter 8 hours working alone and the apprentice 24 hours working alone.