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: 72−8 = 64 km/h = $\dfrac{160}{9}$ m/s.
Relative speed (opposite directions) $= 20 + \dfrac{160}{9} = \dfrac{340}{9}$ m/s.
Sum of lengths $= \dfrac{340}{9} \times 12 = \dfrac{4080}{9} \approx 453.3$ m.
Length of slower train $= 453.3 - 180 = 273.3 \approx \mathbf{273}$ m.
Relative speed (opposite directions) $= 20 + \dfrac{160}{9} = \dfrac{340}{9}$ m/s.
Sum of lengths $= \dfrac{340}{9} \times 12 = \dfrac{4080}{9} \approx 453.3$ m.
Length of slower train $= 453.3 - 180 = 273.3 \approx \mathbf{273}$ m.