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Question 3

A train started from Station A, developed engine trouble and reached Station B, 40 minutes late. What is the distance between Stations A and B?
I. The engine trouble developed after travelling 40 km from Station A and the speed reduced to 1/4th of the original speed.
II. The engine trouble developed after travelling 40 km from station A in two hours and the speed reduced to 1/4th of the original speed.

Solution

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Using first statement alone, we won't be able to find distance as insufficient data is there.
Now using second statement alone, we can find distance d as follows:
velocity before engine failure = $$\frac{40}{2}$$ = 20 km/h and after engine failure = 5 km/hr
And we know total time exceeds 45 min.
Hence 2 + $$\frac{d}{5}$$ = $$\frac{40}{60}$$ + $$\frac{40+d}{20}$$
or $$d = \frac{40}{9}$$  km.

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