Question : Two trains start from stations A and B and travel towards each other at speeds of 16 miles/hour and 21 miles/hour, respectively. At the time of their meeting, the second train had travelled 60 miles more than the first. The distance between A and B (in miles) is:
Option 1: 444 miles
Option 2: 496 miles
Option 3: 333 miles
Option 4: 540 miles
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Correct Answer: 444 miles
Solution :
Let the time at which the trains meet be $x$ hours.
The distance covered by the first train at this time is $16x$ miles and the distance covered by the second train is $21x$ miles.
The second train has travelled 60 miles more than the first.
So, $21x -16x = 60$
$⇒5x = 60$
$⇒x = \frac{60}{5}$
$\therefore x= 12$
So, the trains meet 12 hours after they start.
The total distance between A and B is the sum of the distances travelled by both trains.
$\therefore 16x + 21x = (16 + 21) \times 12 = 37 \times 12 = 444$ miles
Hence, the correct answer is 444 miles.
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