Farhan and Aman are going from Delhi to Haryana. The difference and sum of Their speeds are 40 km/hour and 60 km/hour respectively. If in a race Farhan can finish 8 minutes earlier than Aman, then find the distance they both should cover.

5/3 km

Let the speed of Farhan= F km/h  & Speed of Aman = A km/h and the distance that have to cover be D km.

Then, according to question,

F + A = 60   ---- (1)

F – A = 40   ---- (2)

after adding Equation (1) and (2), we get

2F = 100

F  = 50 km/hour

Put the value of F in equation (1)

F +  A = 60

50 + A = 60

A = 60 – 50

A = 10 km/hour

Time taken by Farhan = \(\frac{D}{50}\)

Time taken by Aman = \(\frac{D}{10}\)

Difference in time = \(\frac{8}{60}\)

\(\frac{D}{10}\) - \(\frac{D}{50}\) = \(\frac{8}{60}\)

\(\frac{5D - D}{50}\) = \(\frac{8}{60}\)

D = \(\frac{5}{3}\) km

So , distance to be covered is \(\frac{5}{3}\) km