Question

$A$ takes $3$ hours more than $B$ to walk a distance of $30$ km. But, if $A$ doubles his pace (speed) he is ahead of $B$ by $1\frac{1}{2}$ hours. Find the speed of $B$.

Answer 1

Let speed of A is $x$ km/hr and that of $B$ is $y$ km/hr.

Time required to walk $30$ km by A is $\frac{30}{x}$ hr and that for B is $\frac{30}{y}$ hr.

Now according to the problem,

$\frac{30}{x}-\frac{30}{y}=3$.......(1).

If $A$ doubles his pace then time required to walk $30$ km is $\frac{30}{2x}$ hr.

Then by the problem,

$\frac{30}{y}-\frac{30}{2x}=\frac{3}{2}$.......(2).

Adding (1) and (2) we get,

$x=\frac{10}{3}$ and using the value of $x$ in (1) we get, $y=5$.

So speed of B is $5$ km/ hr.