Two trains for Mumbai leave Delhi at 6 am and 6.45 am and travel at 100 kmph and 136 kmph respectively. How many kilometers from Delhi will the two trains be together:

Explanation:-

Difference in time of departure between two trains = 45 min. = ⁴⁵/₆₀ hour = ³/₄ hour.
Let the distance be x km from Delhi where the two trains will be together.
Time taken to cover x km with speed 136 kmph be t hour
and time taken to cover x km with speed 100 kmph (As the train take 45 mins. more) be
(t+³/₄)
= (^(4t+3)/₄);

Now,
100 * ^(4t+3)/₄ = 136t;
Or, 25(4t+3) = 136t;
Or, 100t+75 = 136t;
Or, 36t = 75;
Or, t = ⁷⁵/₃₆ = 2.08 hours;
Then, distance x km = 136 * 2.084 = 283.33 km.