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.
Answer & explanation
Correct answer: option 1
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