A tram overtakes 2 persons X and Y walking at an average speed of 3 km/hr and 4 km/hr in the same direction…
A tram overtakes 2 persons X and Y walking at an average speed of 3 km/hr and 4 km/hr in the same direction and completely passes them in 8 seconds and 9 seconds respectively. What is the length of the tram?
15 m
18 m
20 m
24 m
Solution
Let tram speed = $v$ km/hr and length = $L$ m. Relative to X: $L = (v-3)\times\tfrac{5}{18}\times8$. Relative to Y: $L = (v-4)\times\tfrac{5}{18}\times9$. Equating: $8(v-3) = 9(v-4)$, so $8v-24 = 9v-36$, giving $v = 12$ km/hr. Then $L = (12-3)\times\tfrac{5}{18}\times8 = 9\times\tfrac{5}{18}\times8 = 20$ m.