Question

The velocity of a motorboat with respect to still water is $7m{s}^{-1}$ and speed of the stream is $3m{s}^{-1}$. 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
• B. 30 mins
• C. 35 mins
• D. 48.125 mins

Answer 1

Answer: (D)

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 $=\frac{4200}{4}=1050sec$

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 $48.125mins$