A takes 2 hours 30 minutes more than B to walk 40 km. If A doubles

1.	A takes 2 hours 30 minutes more than B to walk 40 km. If A doubles his speed, then he can make it in 1 hour less than B. What is the average time taken by A and B to walk a 40 km distance ?1. 5 hours 15 minutes2. 7 hours 15 minutes3. 6 hours4. 5 hours 45 minutes
Answer» Correct Answer - Option 4 : 5 hours 45 minutes Given: A takes 2 hours 30 minutes more than B to walk 40 km. If A doubles his speed, then he can make it in 1 hour less than B. Formula used: Speed = Distance/Time Calculations: Let the initial speeds of A and B be x and y respectively and the time taken by A and B be t_A and t_B respectively. t_A = 40/x t_B = 40/y t_A - t_{B =} 40/x - 40/y ⇒ 40/x - 40/y = 2.5 ----(i) After A doubles his speed, ⇒ 40/y - 40/2x = 1 ----(ii) On adding equation (i) and (ii), 40/x - 40/2x = 2.5 + 1 ⇒ 40/x - 20/x = 3.5 ⇒ 20/x = 3.5 ⇒ x = 40/7 km/h From equation (ii), 40/y - 40/2x = 1 ⇒ 40/y - 40/2(40/7) = 1 ⇒ 40/y - 7/2 = 1 ⇒ 40/y = 1 + 7/2 ⇒ 40/y = 9/2 ⇒ y = 80/9 km/h tA = 40/x ⇒ tA = 40/(40/7) ⇒ tA = 7 hours tB = 40/y ⇒ 40/(80/9) ⇒ 9/2 hours Average time of A and B = {7 + (9/2)}/2 ⇒ 23/4 hours ⇒ 5 hours 45 minutes ∴ The average time taken by A and B to walk a 40 km distance is 5 hours 45 minutes.

A takes 2 hours 30 minutes more than B to walk 40 km. If A doubles his speed, then he can make it in 1 hour less than B. What is the average time taken by A and B to walk a 40 km distance ?1. 5 hours 15 minutes2. 7 hours 15 minutes3. 6 hours4. 5 hours 45 minutes

Answer» Correct Answer - Option 4 : 5 hours 45 minutes

Given:

A takes 2 hours 30 minutes more than B to walk 40 km.

If A doubles his speed, then he can make it in 1 hour less than B.

Formula used:

Speed = Distance/Time

Calculations:

Let the initial speeds of A and B be x and y respectively and the time taken by A and B be t_A and t_B respectively.

t_A = 40/x

t_B = 40/y

t_A - t_{B =} 40/x - 40/y

⇒ 40/x - 40/y = 2.5 ----(i)

After A doubles his speed,

⇒ 40/y - 40/2x = 1 ----(ii)

On adding equation (i) and (ii),

40/x - 40/2x = 2.5 + 1

⇒ 40/x - 20/x = 3.5

⇒ 20/x = 3.5

⇒ x = 40/7 km/h

From equation (ii),

40/y - 40/2x = 1

⇒ 40/y - 40/2(40/7) = 1

⇒ 40/y - 7/2 = 1

⇒ 40/y = 1 + 7/2

⇒ 40/y = 9/2

⇒ y = 80/9 km/h

tA = 40/x

⇒ tA = 40/(40/7)

⇒ tA = 7 hours

tB = 40/y

⇒ 40/(80/9)

⇒ 9/2 hours

Average time of A and B = {7 + (9/2)}/2

⇒ 23/4 hours

⇒ 5 hours 45 minutes

∴ The average time taken by A and B to walk a 40 km distance is 5 hours 45 minutes.