Question

The Dallas train passes a 200 m long platform in just 40 seconds and a static pole

in 25 seconds. Find the approximate length of the train

Answer 1

Answer:

Length = 333.33 meters

Step-by-step explanation:

Let the length of the train be 'l', and the speed of the train be 's'.

1. First given: When the train passes the 200 m long platform in 40 seconds:

$speed=\frac{distance}{time}$

In this case, the total distance is (200+l) meters.

Therefore,

$s=\frac{200+l}{40}\\200+l=40s\\40s-l=200\:\:\:\:(1)$.

    2. Second given is that the train passes a static pole in 25 seconds:

Distance = l

Speed = s

Time = 25 seconds

Therefore,

$s=\frac{l}{25}\\ l=25s\\25s-l=0\:\:\:\:(2)$.

Now solve equations (1) and (2) simultaneously:

$40s-l=200\\25s-l=0\:\:\:(*-1)\\ \\ 40s-l=200\:\:\:(3)\\-25s+l=0\:\:\:(4)$

Add equations (3) and (4):

$15s=200\\s=\frac{200}{15}\:m/sec$

Substitute by s = 200/15 in equation (2):

$25(\frac{200}{15} )-l=0\\l=333.33\:m$