A boat with a speed of 21 km/hr in still water, travels frompoint A to B in the downstream direction and returns topoint A. Another boat with speed of 28 km/hr travels from Bto A and returns to point B. The difference between the timetaken by them to cover the distance is 6.5 hrs. What is thedistance between points A and B, if the speed of stream is 7km/hr?(a) 420 km(b) 120 km(c) 280 km
Question
A boat with a speed of 21 km/hr in still water, travels frompoint A to B in the downstream direction and returns topoint A. Another boat with speed of 28 km/hr travels from Bto A and returns to point B. The difference between the timetaken by them to cover the distance is 6.5 hrs. What is thedistance between points A and B, if the speed of stream is 7km/hr?(a) 420 km(b) 120 km(c) 280 km
Solution
Let's solve this step by step:
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The speed of the first boat in downstream (i.e., along the direction of the stream) is the speed of the boat plus the speed of the stream. So, it's 21 km/hr + 7 km/hr = 28 km/hr.
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The speed of the first boat in upstream (i.e., against the direction of the stream) is the speed of the boat minus the speed of the stream. So, it's 21 km/hr - 7 km/hr = 14 km/hr.
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The speed of the second boat in both downstream and upstream is 28 km/hr, because it's not affected by the stream.
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Let's denote the distance between points A and B as D. The time taken by the first boat to travel from A to B and back to A is D/28 + D/14. The time taken by the second boat to travel from B to A and back to B is 2D/28.
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According to the problem, the difference between the time taken by the first boat and the second boat is 6.5 hours. So, we have the equation: D/28 + D/14 - 2D/28 = 6.5.
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Solving this equation, we get D = 420 km.
So, the distance between points A and B is 420 km. The correct answer is (a) 420 km.
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