Two boats start together and race across a 50-km-wide lake and back. Boat A goes across at 50 km/h and returns at 50 km/h. Boat B goes across at 25 km/h, and its crew, realizing how far behind it is getting, returns at 75 km/h. Turnaround times are negligible, and the boat that completes the round-trip first wins.

Required:

a. Which boat wins?

b. What is the average velocity of the winning boat?

Boat A wins and 50km/hr

Explanation:

To solve this problem we need to calculate the time required for both boats to make the round trip.

For Boat A.

The time required for the first trip = distance / speed = 50/50 = 1h

For the return trip the time is same since it's the same distance on the same speed.

Hence the time taken for boat A to make the round trip is 2hrs.

For boat B,

The time required for the first trip = distance / speed = 50/25 = 2h

The time for the return trip is;

=distance / speed = 50/75 = 2/3h = 2/3*60 = 40mins

By comparing both time.

Boat A requires less time hence Boat A wins.

2. The average velocity of the winning boat is the velocity of boat A.

Which is total distance / total time for the trip.

100km/2hrs = 50km/hr