A train overtakes two runners moving in the same direction at speeds of 5 km/h and 7 km/h, passing them completely in 18 seconds and 20 seconds, respectively. What is the length of the train (in metres)?
100
Let the train's speed be \(v\) km/h and its length be \(L\) metres.
Relative speed with the 5 km/h runner is \((v-5)\) km/h, so \(L = (v-5) \times \frac{5}{18} \times 18 = (v-5) \times 5\) metres (converting 18 s to hours and simplifying).
Relative speed with the 7 km/h runner is \((v-7)\) km/h, so \(L = (v-7) \times \frac{5}{18} \times 20\).
Equating the two expressions: \((v-5) \times 18 = (v-7) \times 20\), which gives \(18v - 90 = 20v - 140\), so \(2v = 50\), hence \(v = 25\) km/h.
Length: \(L = (25-5) \times \frac{5}{18} \times 18 = 20 \times 5 = 100\) metres.
Hence, the length of the train is 100 metres.
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Important Questions from Problem on Trains
A train is to cover 370 km at a uniform speed. After running 100 km, the train could run at a speed 5 km/h less than its normal speed due to some technical fault. The train got delayed by 36 minutes. What is the normal speed of the train, in km/h?
A train travelling at 36 km/h crosses a pole in 25 seconds. How much time (in seconds) will it take to cross a bridge 250 m long?
A train covers 450 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less to cover the same distance. How much time will it take to cover 315 km at its usual speed?
A train crosses a pole in 12 sec, and a bridge of length 170 m in 36 sec. Then the speed of the train is:
The ratio of the speeds of two trains is 2 : 7. If the first train runs 250 km in 5 hours, then the sum of the speeds (in km/h) of both the trains is:
