Lesson A train passing a telegraph post and passing a bridge

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A train passing a telegraph post and passing a bridge


Problem 1

A train takes 4 seconds to pass a telegraph post and 20 seconds to pass a 256 m long bridge.
Find the length of the train and its speed.

Solution

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

L%2Fu = 4.

Since the train passes a  256 m long bridge in  20 seconds,  it gives you another equation

%28256+%2B+L%29%2Fu = 20

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

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

system+%28L%2Fu+=+4%2C%0D%0A%28256+%2B+L%29%2Fu+=+20%29.

Express  L  from the first equation  L = 4u  and then substitute it into the second equation.  You will get

%28256+%2B+4u%29%2Fu = 20.

Simplify it step by step:

256 + 4u = 20u,

256 = 20u - 4u,

256 = 16u,

u = 256%2F16 = 16.

Thus the train's speed is  16 m%2Fs = 57.6 km%2Fh.

It implies that the train's length is  L = 4u = 4%2A16 = 64 m.

Answer.  The train's length is  64 m.  The train's speed is  16 m%2Fs.


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- Travel and Distance problems for two bodies moving in the same direction (catching up)
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    - One more problem on calculating an average speed

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Use this file/link  ALGEBRA-I - YOUR ONLINE TEXTBOOK  to navigate over all topics and lessons of the online textbook  ALGEBRA-I.

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