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Two boats A and B are of length 100 m and 65 m respectively. The boat A travels a distance of 300 m in 10 seconds in downstream and the boat B travels the same distance in 12 seconds in upstream. The speed of the stream is 5 m/second. Find the time taken by these boats to cross each other where A travels in downstream and B travels in upstream. 

Two boats A and B are of length 100 m and 65 m respectively. The boat A travels a distance of 300 m in 10 seconds in downstream and the boat B travels the same distance in 12 seconds in upstream. The speed of the stream is 5 m/second. Find the time taken by these boats to cross each other where A travels in downstream and B travels in upstream.  Correct Answer 3 seconds

Given:

Two boats A and B are of length 100m and 65m respectively

The boat A travels a distance of 300m in 10 seconds

The boat B travels the same distance in 12 seconds in upstream

The stream is 5 m/second

Formula used: Distance = Speed × Time, (s = v × t)

Calculation:

Let the speed of boat A in still water be x m/s

And let the speed of boat B in still water be y m/s

So the speed of boat A in downstream is (x + 5) m/s

And the speed of boat B in upstream is (y – 5) m/s

According to question,

300 = (x + 5) × 10

⇒ x = 25 m/s

And also

300 = (y – 5) × 12

⇒ y = 30 m/s

A travels in downstream and B travels in upstream

So, the speed of boat A in downstream is (25 + 5) = 30 m/s

And the speed of boat B in upstream is (30 – 5) = 25 m/s

∴  Time taken by boats A and B to cross each other = (100 + 65)/(30 + 25) = 165/55 = 3 seconds.

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