Ratio and Proportion Word Problems: Train
It took a train seconds to completely pass a -m iron bridge. When the train was passing through a -m tunnel, it was invisible from outside of the tunnel for seconds. If the speed of the train was constant, what was the length of the train (in meters)?
Details and Assumptions:
- The train passes the iron bridge when no part of the train is on the bridge.
- The train is invisible from outside of the tunnel when no part of the train is outside of the tunnel.
The answer is 460.
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1 solution
Let x be the length (in meters) of the train. Then it must run ( 5 0 0 + x ) m to completely pass a 5 0 0 m iron bridge. On the other hand, it runs ( 1 9 0 0 − x ) m while the whole length of it stays inside the 1 9 0 0 m tunnel so that it is invisible from outside. Since the train is running at a constant speed,
2 0 5 0 0 + x = 3 0 1 9 0 0 − x
⇒ ( 5 0 0 + x ) × 3 0 = ( 1 9 0 0 − x ) × 2 0
⇒ 5 0 x = 3 8 0 0 0 − 1 5 0 0 0
⇒ x = 4 6 0 .