A car and bus were travelling in same direction. At 8:30 AM the car travelling at a speed of 72 km/h was 8.4 km behind the bus. At 9:15 AM the car was 31.6 km ahead of bus. What is ratio of speed of car to the speed of the bus?
Answer & explanation
Correct answer: option 2
Let bus speed = S, time b/w 8:30 AM and 9:15 AM = 45 mins
total distance = 31.6 + 8.4 = 40 km
Relative speed = 72 - S
40 = (72 - S) × \(\frac{45}{60}\) = (72 - S) × \(\frac{3}{4}\)
40 = 72 × \(\frac{3}{4}\) - \(\frac{3}{4}\)S
40 = 54 - \(\frac{3}{4}\)S
⇒ \(\frac{3}{4}\)S = 54 - 40
⇒ S = \(\frac{14 × 4}{3}\)
ratio → speed of car : speed of bus
72 : \(\frac{14 × 4}{3}\)
27 : 7