Question

The velocity of a motor boat with respect to still water is 7 ms- and velocity of water in a river is
3 ms. When the boat starts moving upstream a float was dropped from it. The boat travels 4.2 km and
returns and reaches the float. The time taken by the boat to catch the float is

1) 25 min
2) 30 min
3) 35 min
4) 40 min

Answer 1

Correct answer:-

option 4) 40 mins.

OR

48.125 mins.

Explanation:-

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

=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 48.125 mins. [Ans].

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Answer 2

correct option is 3)35 min