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# [Smart Math] Time Speed Distance Problem 11

Here’s and example of a SMART MATH problem for TIME SPEED DISTANCE.

### Problem

A train speeds past a pole in 20 seconds and speeds past a platform 150 meters long in 60 seconds. What is the length of the train?

1. 75 meters
2. 100 meters
3. 150 meters
4. 200 meters
5. 250 meters

### The Usual Method

Let ‘x’ meters be the length of the train and ‘s’ be its speed in mt/sec (meters per second).

Hence, $\frac{x}{20}=s$ (Since, it takes 20 seconds to pass its length with respect to the pole)

Also, $\frac{x+150}{60}=s$

$\therefore \frac{x}{20}=\frac{x+150}{60}$

$\therefore 3x=x+150$

$\therefore x=\frac{150}{2}=75$meters

(Ans: 1)

Estimated Time to arrive at the answer = 30 seconds.

### Using Technique

Since the time taken by the train to cover the platform is 3 times the time it takes to cover the pole, the total length that the train traverses while crossing the platform is three times of what it does while traversing the pole.

When the train traverses the pole, its traverses its own length and when it traverses the platform, it traverses its length and the length of the platform, hence if ‘l’ is the length of the train, then:

$3l=l+150$

$\therefore l=75$meters

(Ans: 1)

Estimated Time to arrive at the answer = 10 seconds.

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