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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 minutes
2. 7 hours 15 minutes
3. 6 hours
4. 5 hours 45 minutes

1 Answer

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Best 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 tA and tB respectively.

tA = 40/x

tB = 40/y

tA - tB = 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.

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