10. A train leaves a station A at 7 am and reaches another
station B at 11 am. Another train leaves B at 8 am and
reaches A at 11.30 am. The two trains cross one
another at
Answers
9 am is the answer man
The two trains cross one another at 9:24 a.m.
Step-by-step explanation:
Step 1:
Let the train travelling from A to B be “Train 1” and the train travelling from B to A “Trian 2”.
Since Train 1 starts at 7:00 a.m. and reaches at 11:00 a.m.
So, the time taken by Train 1 from A to B = 4 hours
Also, Train 2 starts at 8:00 a.m. and reaches at 11:30 a.m.
So, the time taken by Train 2 from B to A = 3.5 hours
Step 2:
Let the distance between A & B = L.C.M of (4 and 3.5) = 28 km
Therefore,
The speed of Train 1 = 28/4 = 7 km/hr
And,
The speed of Train 2 = 28/3.5 = 8 km/hr
From the question, we can see that Train 1 starts 1 hr early than Train 2, so,
The distance covered by Train 1 in 1 hr = 7 x 1 = 7 km ← by this time Train 2 starts at 8:00 a.m.
∴ The remaining distance between the two trains at 8:00 a.m. = 28 - 7 = 21 km
Step 3:
Since the trains are moving in opposite directions, therefore,
Their relative speed will be = 7 + 8 = 15 km/hr
∴ The time taken by the two trains to cross each other is given by,
= [distance] / [speed]
= [21/15] hr
= [21/15] * 60 minutes
= 21 * 4 minutes
= 84 minutes from 8:00 a.m.
Thus,
Their final time of the crossing each other will be → 8:00 + 1 hr 24 minutes → 9:24 a.m.
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