ajit257 wrote:

Two trains X and Y started simultaneously from opposite ends of a 100 mile route and travelled toward each other on parallel tracks. Train X travelling at a constant rate completed the 100 mile trip in 5 hours. Train Y travelling at constant rate completed the 100 mile trip in 3 hours. How many miles had train X travelled when it met train Y ?

Can someone please explain the concept behind this type of problem ? All help appreciated.

The concept used in these questions is Relative Speed.

If two people walk in opposite directions (either towards each other or away from each other), their speed relative to each other is the sum of their speeds. e.g. If you are walking away from me at a speed of 2 miles/hr and I am walking away from you at a speed of 1 mile/hr, together we are creating a distance of 3 miles in 1 hr between us so our relative speed is 2 + 1 = 3 miles/hr

On the other hand, when two people walk in the same direction, their relative speed is the difference between their speeds.

e.g. if you are walking away from me at 1 mile/hr and I am walking towards you at 2 miles/hr, my speed relative to you is 2-1 = 1 mile/hr.

Time taken to meet = Total distance traveled/Relative speed

Speed of train X = 100/5 = 20 miles/hr

Speed of train Y = 100/3 miles/hr

Relative Speed = 20 + 100/3 = 160/3 miles/hr

Distance between them = 100 miles

Time taken to meet = 100/(160/3) hr = 15/8 hrs

In this time, train X would have traveled 20 * (15/8) = 37.5 miles

Faster Alternate Approach using Ratios :

Time taken by train X : Time taken by train Y = 5:3

Then, Speed of train X:Speed of train Y = 3:5

Since they start simultaneously, they travel for same time. So the ratio of their distance covered should be same as ratio of their speeds.

Distance covered by train X : Distance covered by train Y = 3:5

3/8 *100 = 37.5 miles (Distance covered by train X)

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