SOLUTION: A train takes 4sec to pass a telegraph post and 20sec to pass a 264m long bridge.let us find the length of train and also its speed.

Question 983846: A train takes 4sec to pass a telegraph post and 20sec to pass a 264m long bridge.let us find the length of train and also its speed.
Found 2 solutions by macston, ikleyn:
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
.
Consider the telegraph post at one end of the bridge.
To pass the bridge, the engine first goes on, and the train is not past the bridge until the rear goes off the other end. When the front passes the telegraph pole (goes on the bridge), 4 seconds pass before the rear goes on the bridge (passes the pole). The rear of the train must pass off the bridge 20 seconds after the engine goes on, or 16 seconds after the rear goes on (20 seconds-4 seconds for the whole train to pass the pole). The rear must travel 264m in 16 seconds, or 16.5 meters/second.
ANSWER: 1: The speed of the train is 16.5 meters per second.
.
Traveling at 16.5m/s, it takes 4 seconds to pass the pole, so the length of the train is (4s)(16.5m/s)=66 meters.
ANSWER 2: The train is 66 meters long.
Answer by ikleyn(52802) (Show Source): You can put this solution on YOUR website!

Let L be the train's length (in meters) and let u be the train's speed (in meters per second).

Since the train takes 4 seconds to pass a telegraph post, it gives an equation

= .

Since the train passes a 264 m long bridge in 20 seconds, it gives you another equation

=

(the train should move the distance equal to the bridge length plus its own length - it means "to pass the bridge").

Thus you need to solve the system of two equations in two unknowns

.

Express L from the first equation = and then substitute it into the second equation. You will get

= .

Simplify it step by step:

264 + 4u = 20u,

264 = 20u - 4u,

264 = 16u,

= = .

Thus the train's speed is 16.5 .

It implies that the train's length is = = = .

Answer. The train's length is 66 m. The train's speed is 16.5 .

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