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?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e 5 hours 45 minutes.
We know that,
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 tA and tB respectively.
tA = 40/x
tB = 40/y
tA - tB = 40/x - 40/y
⇒ 40/x - 40/y = 2.5 .....(1)
After A doubles his speed,
⇒ 40/y - 40/2x = 1.............(2)
On adding equations (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 (2),
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
Hence, The average time taken by A and B to walk a 40 km distance is 5 hours 45 minutes.