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A train crosses a bridge at a speed of x m/sec in one min. and a pole at 2x m/sec in 8 sec. If length of the bridge is 660 m. How many seconds does it take to cross the bridge at 3x m/sec.

A train crosses a bridge at a speed of x m/sec in one min. and a pole at 2x m/sec in 8 sec. If length of the bridge is 660 m. How many seconds does it take to cross the bridge at 3x m/sec. Correct Answer 20 sec

Given:

Speed of train to cross a bridge = x m/sec

Time taken by train to cross the bridge with speed of x m/s = 60 sec

Speed of train to cross the pole = 2x m/sec

Time taken by train to cross the pole with the speed of 2x m/s = 8 sec

Length of bridge = 660 m

Formula used:

Time = Distance/Speed

Concept used:

If a train crosses a bridge or any other horizontal object, distance travelled by train would be the sum of length of the bridge and the length of the train

If any train crosses a man/pole or any other vertical object, distance travelled by train is equal to length of the train

Calculations:

Distance travelled by train to cross the pole = 2x × 8 = 16x

length of train = 16x

Distance travelled by train to cross the bridge = 60 × x = 60x

⇒ 60x = 660 + 16x

⇒ 44x = 660

⇒ x = 15 m/sec

Length of train = 16 × 15 = 240 m

Now, speed of train = 3x = 3 × 15 = 45 m/sec

Time taken to cross the bridge = (660 + 240) /45 = 20 sec

∴ Time taken to cross the bridge with the speed 3x m/s is 20 sec

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