Question

A carpenter can do a job in four hours. His assistant can do the same job in six hours. How long would it take them to do the job together?

Answer 1

if the carpenter can do the whole job in 4 hours, that means in 1 hour, it has only done 1/4 of the whole thing.

if his assistant can do the job in 6 hours, that means, in 1 hour, he has done only 1/6 of the whole job.

let's say if both of them work together, they can do the job in "t" hours, so in 1 hour alone, the carpenter has done 1/4 of it, and the assistant has done 1/6 of it, for a total of 1/t of the job.

$\bf \stackrel{\textit{carpenter's rate}}{\cfrac{1}{4}}+\stackrel{\textit{assistant's rate}}{\cfrac{1}{6}}~~=~~\stackrel{\textit{total done}}{\cfrac{1}{t}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{3+2}{12}=\cfrac{1}{t}\implies \cfrac{5}{12}=\cfrac{1}{t}\implies 5t=12\implies t=\cfrac{12}{5}\implies \stackrel{\textit{2 hours and 24 minutes}}{t=2\frac{2}{5}}$

Answer 2

2 hours and 24 minutes because if you choose like 24 then it would be 24/10 hours