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?

5 hours 45 minutes

Let speed of A = a km/h

Time taken by A to cover 40 km = \(\frac{40}{a}\)

Time taken by B to cover 40 km = \(\frac{40}{a}\) - 2.5

If A doubles his Speed , Time taken = \(\frac{40}{2a}\)

According to question ,

(\(\frac{40}{a}\) - 2.5) - \(\frac{40}{2a}\) = 1

\(\frac{40}{2a}\) = 3.5

a = \(\frac{40}{7}\)

Time taken by A = \(\frac{40 × 7}{40}\) = 7 hours

Now  , Time time taken by B = \(\frac{40}{a}\) - 2.5 = 7 - 2.5

= 4.5 hours

Average of time taken by A & B = \(\frac{7 + 4 .5}{2}\) 

= \(\frac{11.5}{2}\)  = 5 hours 45 minutes