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 speeds of A and B.

Answer 1

Let the speed of A be x km/h and that of B be y km/h.

According to the question, 30/x = 30/y + 3

Also, 30/2x = 30/y - 3/2

Substituting 1/x= p and 1/y = q in the equations, we get

30p = 30q + 3

$\Rightarrow$ 10p - 10q = 1......(1)

and 15 p = 30q - 3/2

$\Rightarrow$ 10 q - 1/2 = 5p

$\Rightarrow$ 20q - 1 = 10 p

$\Rightarrow$ 20q -10 p = 1....(2)

Solving equations (1) and (2), we get p =3/10 and q = 1/5

So, x = 10/3 km/h and y = 5 km/h.