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}}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Bcarpenter%27s%20rate%7D%7D%7B%5Ccfrac%7B1%7D%7B4%7D%7D%2B%5Cstackrel%7B%5Ctextit%7Bassistant%27s%20rate%7D%7D%7B%5Ccfrac%7B1%7D%7B6%7D%7D~~%3D~~%5Cstackrel%7B%5Ctextit%7Btotal%20done%7D%7D%7B%5Ccfrac%7B1%7D%7Bt%7D%7D%0A%5C%5C%5C%5C%5B-0.35em%5D%0A%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%0A%5Ccfrac%7B3%2B2%7D%7B12%7D%3D%5Ccfrac%7B1%7D%7Bt%7D%5Cimplies%20%5Ccfrac%7B5%7D%7B12%7D%3D%5Ccfrac%7B1%7D%7Bt%7D%5Cimplies%205t%3D12%5Cimplies%20t%3D%5Ccfrac%7B12%7D%7B5%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7B2%20hours%20and%2024%20minutes%7D%7D%7Bt%3D2%5Cfrac%7B2%7D%7B5%7D%7D)