Two trains running in opposite directions on parallel tracks cross each other in 12 seconds. The faster train is 180 m long and crosses a lamp post in 9 seconds. If the slower train's speed is 8 km/h less than the faster train's, what is the length of the slower train, in metres (closest integer)?
Answer and solution
Correct answer: 273
Solution
Faster train: $\dfrac{180}{9} = 20$ m/s $= 72$ km/h. Slower: $64$ km/h $= \dfrac{160}{9}$ m/s
Relative speed $= 20 + \dfrac{160}{9} = \dfrac{340}{9}$ m/s
Combined length $= \dfrac{340}{9} \times 12 = \dfrac{1360}{3}$ m
Slower train $= \dfrac{1360}{3} - 180 = \dfrac{820}{3} = 273\tfrac{1}{3} \approx 273$ m
Relative speed $= 20 + \dfrac{160}{9} = \dfrac{340}{9}$ m/s
Combined length $= \dfrac{340}{9} \times 12 = \dfrac{1360}{3}$ m
Slower train $= \dfrac{1360}{3} - 180 = \dfrac{820}{3} = 273\tfrac{1}{3} \approx 273$ m