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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:

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Solution

The correct option is **B** 48.125 mins

Speed of the boat when it travels upstream =7−3=4m/sec

Speed of the boat when it travels downstream =7+3=10m/sec

Now,

As soon as the float falls, it will travel downstream at the speed of 3m/sec

And in the meantime, the boat has also traveled upstream a distance of 4.2 km

So,

Time spend on traveling upstream by boat =42004=1050sec

In the meantime, the float would had traveled downstream by =1050×3 = 3150 m

Hence, the total distance between the float and the boat will be =3150 + 4200 = 7350 m

Now, the relative speed between a boat and the float =10-3=4 m/sec

Hence time taken = 7350/4=1837.5 sec

Hence, total time spent = 1837.5+1050=2887.5 sec

This is 2887.5 /60= 48.125 mins

Hence the float and the boat will meet in 48.125mins

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