Would You Travel in a Goods Train?
A Goods Train crosses a
long bridge with uniform speed
in
seconds.
Then, if it were to cross a long bridge with uniform speed , it would require ______
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1 solution
If a train crosses a bridge, it would require time to cover both - the distance of the bridge as well as its own length l (it won't suffice if only the driver crosses without the train!).
⇒ total distance covered on the 1 2 0 m bridge = 1 2 0 + l . Therefore, time required to cross the 1 2 0 m bridge = v 1 2 0 + l = t . which can be written as v 1 2 0 + v l .
Now, total distance covered on the 2 4 0 m bridge = 2 4 0 + l . Therefore, time required to cross the 2 4 0 m bridge = 2 v 2 4 0 + l . which can be written as 2 v 2 4 0 + 2 v l ⇒ v 1 2 0 + 2 v l .
Notice that the first term is same (i.e. v 1 2 0 ), but the second term is larger in the second expression (i.e. 2 v l < v l ).
⇒ 2 v 2 4 0 + 2 v l < t .