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?

27 : 7

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