Question

A man had to walk a certain distance. He covered two thirds of it at $4$ kmph and the remaining at $5$ kmph. If the total time taken is $42$ minutes, find the total distance.

Answer 1

Let the distance be '$x$' km.
Therefore total time taken $=\frac{2x}{12}+\frac{x}{15}$ hr
$\Rightarrow$ $(\frac{2x}{12}+\frac{x}{15})$hr $=42$ min.
$\Rightarrow$ $(\frac{2x}{12}+\frac{x}{15})$ hr $=\frac{42}{60}$ hr
$\frac{2x}{12}+\frac{x}{15}=\frac{42}{60}$
$\frac{10x+4x}{60}=\frac{42}{60}$
$\Rightarrow$ $14x=42$
$\Rightarrow$ $x=3$
Total distance $x=3km$