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

**Problem**

**Problem**

A train traveling at 36 km/hr completely passes another train at 50% more speed but 50% of its length in the opposite direction in 12 secs. It takes 90 secs for the same train to pass a platform. Find the length of the platform.

- 700 meters
- 900 meters
- 950 meters
- 1000 meters
- 1100 meters

**The Usual Method**

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Speed of slower train = 36 km/hr = 10 mt/sec

Speed of faster train = 36 x 1.5 = 54 km/hr = 15 mt/sec

Let the length of the slower train be 2*l*.

length of the faster train =

Using the concept of relative speed, we get:

meters

Let the length of the platform be ‘*x*’ meters.

Using relative speed concepts, we get:

meters

**(Ans: 1)**

*Estimated Time to arrive at the answer = 45 seconds.*

**Using Technique**

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Note that it takes 90 secs for the train traveling at the speed of 10 mt/sec (36 km/hr) to traverse a length equal to its own plus that of the platform.

i.e. length of train + length of platform = 90

aaaaaaaaaaaaaaa10

length of train + length of platform = 90 x 10 = 900 meters.

Hence, the length of platform has to be < 900 meters. Hence 700 meters (option ‘1’).

**(Ans: 1)**

*Estimated Time to arrive at the answer = 10 seconds.*

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