Question

A takes 3 hrs more than B to walk 30 km. but, if A doubles his pace, he is ahead of B by
1.5 hrs. Find their speed of walking
Please tell

Answer 1

Given data : A takes 3 hrs more than B to walk 30 km. but, if A doubles his pace, he is ahead of B by 1.5 hrs.

To find : Find the speed of walking of A and B.

Solution : Let, time taken by A to cover 30 km be x and time taken by B to cover 30 km be y.

When, A takes 3 hrs more than B to walk 30 km. Then;

⟹ Time taken by A = (y + 3) hr

⟹ Distance covered by A = 30 km

Now, by formula speed

⟹ speed of A = distance/time

⟹ speed of A = 30/(y + 3) -----{ 1 }

When, A doubles his pace, he is ahead of B by 1.5 hrs. Then;

⟹ Time taken by A = (y - 1.5) hr

⟹ Distance covered by A = 30 km

Now, by formula speed

⟹ speed of A = distance/time

⟹ 2(speed of A) = 30/(y - 1.5)

Now, by formula speed

⟹ speed of A = 15/(y - 1.5) -----{ 2 }

Now, from eq. { 1 } and eq. { 2 }

⟹ 30/(y + 3) = 15/(y - 1.5)

⟹ 30 * (y - 1.5) = 15 * (y + 3)

⟹ 30y - 45 = 15y + 45

⟹ 30y - 15y = 45 + 45

⟹ 15y = 90

⟹ y = 90/15

⟹ y = 6 hour

Hence, time taken by B is 6 hour.

Now, put value of y in eq. { 1 }

⟹ speed of A = 30/(y + 3)

⟹ speed of A = 30/(6 + 3)

⟹ speed of A = 30/9

⟹ speed of A = 10/3 km/hr or 3.33 km/hr

We know,

⟹ time taken by B = 6 hour

⟹ distance covered by B = 30 km

Now, by formula of speed

⟹ speed of B = distance/time

⟹ speed of B = 30/6

⟹ speed of B = 5 km/hr

Answer : Hence, time taken by A is 10/3 km/hr and speed of B is 5 km/hr.