Two trains for Patna leave Delhi at 6 a.m. and 6:45 a.m. and travel at 98 kmph and 136 kmph respectively. How many kilometres from Delhi will the two trains meet?
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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.
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.
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