Question

Rajeev started to move from point A towards point B exactly an hour after Rohit started from B in the opposite direction but at a speed twice as much as that of Rohit. By the time Rohit covered one sixth of the distance between the points B and A, Rajeev also covered the same distance: How many more hours would Rohit (compared to Rajeev) take to complete his journey

Answer 1

2 more hours

Explanation:

speed = distance/time = d/t

Let:

Sro = Rohit speed

Sra = Rajeev speed

Tro = Rohit time

Tra = Rajeev time

D = distance Point A to B (and B to A)

Solution:

Sro = (D/6)/Tro

Tro = (D/6)/Sro = D / (6Sro)

Sra = 2(Sro) = D / Tra

Tra = 1/6(D/2Sro) = D / 12Sro

D/6Sro - D/12Sro = 1 (the difference in start time is 1 hr, which was given)

Multiply the expression by 12Sro on both sides and simplify

2D - D = 12Sro

D = 12Sro

Tro = D/6Sro = 12Sro/6Sro = 2

Therefore, it takes Rohit 2 more hours compared to Rajeev to complete his journey