Discussion
A train running between two stations A and B arrives at its destination 10 minutes late when its speed is 50 km/h and 50 minutes late when its speed is 30 km/h. What is the distance between the stations A and B ?
Answer: D
The distance is 50 km.
Let the distance be \(d\) km. The two journeys differ by 40 minutes, \(\frac{2}{3}\) hour, because the train is 10 minutes late in one case and 50 in the other:
\[ \begin{aligned} \frac{d}{30} - \frac{d}{50} &= \frac{2}{3} \\ \frac{5d - 3d}{150} &= \frac{2}{3} \\ 2d &= 100,\ d = 50 \end{aligned} \]
Check: at 50 km/h it takes 60 minutes, at 30 km/h 100 minutes, a difference of 40 minutes, so the right time is 50 minutes in both cases. 40, 48 and 60 km give time differences of 32, 38.4 and 48 minutes.
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