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The speeds of two boats A and B travelling upstream are 40 m/h and 65 m/h. The speed of current is 10 m/h. Boat A is 10 m ahead of boat B. Both the boats start at the same time downstream, find the time after which boat B will catch boat A.

The speeds of two boats A and B travelling upstream are 40 m/h and 65 m/h. The speed of current is 10 m/h. Boat A is 10 m ahead of boat B. Both the boats start at the same time downstream, find the time after which boat B will catch boat A. Correct Answer 24 minutes

Upstream speed of boat A  = 40 m/h

Upstream speed of boat B = 65 m/h

Speed of current = 10 m/h

Speed of boat A in still water = 40 + 10 m/h = 50 m/h

Speed of boat B in still water = 65 + 10 m/h = 75 m/h

Speed of boat A downstream = 50 + 10 m/h = 60 m/h

Speed of boat B downstream = 75 + 10 m/h = 85 m/h

Speed of boat B with respect to boat A = 85 – 60 m/h = 25 m/h

∵ Boat B has to cover 10 m to catch boat A,

∴ Time after which boat B catches boat A = 10/25 h = 0.4 h = 24 minutes

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