Question

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

Answer 1

Step-1: Find the work done in one hour:

It is given that a carpenter can do a job in $8\mathrm{hour}$ .

Thus, the carpenter can do $\frac{1}{8}$ of a job in $1\mathrm{hour}$.

Similarly, it is given that carpenter's assistant can do a job in $10\mathrm{hour}$.

Thus, the carpenter's assistant can do $\frac{1}{10}$ of a job in $1\mathrm{hour}$.

Step-2: Find the time:

Let us assume that the carpenter and his assistant can do the job in $x\mathrm{hour}$.

Thus, the carpenter and his assistant can do $\frac{1}{x}$ of the job in $1\mathrm{hour}$.

Thus,

$$\begin{gathered} \frac{1}{x}=\frac{1}{8}+\frac{1}{10} \\ \Rightarrow \frac{1}{x}=\frac{5+4}{40}\left[\mathrm{L}.\mathrm{C}.\mathrm{M}\mathrm{of}(8,10)\mathrm{is}40\right] \\ \Rightarrow \frac{1}{x}=\frac{9}{40} \\ \Rightarrow 40=9x\left[\text{Cross multiply the equation}\right] \\ \Rightarrow \frac{40}{9}=\frac{9x}{9}\left[\text{Divide both side of the equation by 9}\right] \\ \Rightarrow \frac{40}{9}=x \\ \Rightarrow x=\frac{40}{9} \\ \therefore x=4\frac{4}{9}\mathrm{hour} \end{gathered}$$

Hence, the time taken by the carpenter and his assistant to do the job is $4\frac{4}{9}\mathrm{hour}$.