Question

A man can do a job in $h$ hours alone and his son can do it in $2h$ hours alone. Together, how many hours will it take them to do the job?

• A. $3h$
• B. $\frac{h}{3}$
• C. $\frac{3h}{2}$
• D. $\frac{2h}{3}$
• E. $\frac{h}{2}$

Answer 1

The correct option is D $\frac{2h}{3}$

Let the job is $x$

$x$ job finished by son in $=2h$ hours

$x$ job finished by man in $=h$ hours

work rate of man$=\frac{x}{2h}$

work rate of son$=\frac{x}{h}$

work rate of (man $+$ son)$=\frac{x}{2h}+\frac{x}{h}$$=\frac{3x}{2h}$

so x work will finish in $=$ when (man $+$son) work together$=\frac{2h}{3}$.