# CAT Practice : Speed Time, Races

## Trains A and B

Q.27: Two trains start together from a Station A in the same direction. The second train can cover 1.25 times the distance of first train in the same time. Half an hour later, a third train starts from same station and in the same direction. It overtakes the second train exactly 90 minutes after it overtakes the first train. What is the speed of third train, if the speed of the first train is 40 Km/hr?
1. 20 Km/hr
2. 50 Km/hr
3. 60 Km/hr
4. 80 Km/hr

Choice C.60 Km/hr

## Detailed Solution

Speed of Train B = Sb = 1.25 x Sa = 1.25 x 40 = 50 Km/hr

In half an hour, Train A would have mover = $40 * \frac{1}{2}$ = 20 Km away from train C .

Therefore, train C will have to cover 20 Km in relative speed to cross train A. So, time taken = $\frac{20}{(S_c - 40)}$ (Sc - 40 Km/hr is the relative speed of train C w.r.t A)

Similarly, train C will have to cover $50 * \frac{1}{2}$ = 25 Km in relative speed to cross train B. So, time taken = $\frac{25}{(S_c - 50)}$.

Given the difference between these two times is 90 minutes. Therefore, $\frac{25}{(S_c - 50)} - \frac{20}{(S_c - 40)} = \frac{90}{60} = \frac{3}{2}$.

Now, instead of solving this equation, one can quickly put in the options in this equation to find Sc = 60 Km/hr.

Note - You should be able to rule out A and B beforehand because speed of train Chas to be greater than Train A and B to overtake them.

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## More questions from Speed Time, Races

"Life is a race ... if you don't run fast ... you will be like a broken undaa" - Veerusahasra Buddhi