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Question

# The velocity of a motorboat with respect to still water is 7ms−1 and speed of the stream is 3ms−1. When the boat starts moving upstream a float was dropped from it. The boat travels 4.2 km up stream turned about and caught up with the float. The time is taken by the boat to reach the float is:

A
25 mins
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B
30 mins
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C
35 mins
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D
48.125 mins
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Solution

## The correct option is B 48.125 minsSpeed of the boat when it travels upstream =7−3=4m/secSpeed of the boat when it travels downstream =7+3=10m/secNow,As soon as the float falls, it will travel downstream at the speed of 3m/secAnd in the meantime, the boat has also traveled upstream a distance of 4.2 kmSo,Time spend on traveling upstream by boat =42004=1050secIn the meantime, the float would had traveled downstream by =1050×3 = 3150 mHence, the total distance between the float and the boat will be =3150 + 4200 = 7350 mNow, the relative speed between a boat and the float =10-3=4 m/secHence time taken = 7350/4=1837.5 secHence, total time spent = 1837.5+1050=2887.5 sec This is 2887.5 /60= 48.125 minsHence the float and the boat will meet in 48.125mins

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