Two boats start together and race across a 60-km-wide lake and back. Boat A goes across at 60 km/h and returns at 60 km/h. Boat B goes across at 30 km/h, and its crew, realizing how far behind it is getting, returns at 90 km/h. Turnaround times are negligible, and the boat that completes the round trip first wins. (a) Which boat wins and by how much? (Or is it a tie?) (b) What is the average velocity of the winning boat?

(a) Boat A wins the race by 40 min.

(b) Average speed of Boat A is 60 km/hr.

Explanation:

Given-

Distance for Boat A and Boat B, d = 60 km

Speed of the Boat A while going, s = 60 km/h

Speed of the Boat A while returning, s = 60 km/h

Speed of the Boat B while going, s = 30 km/h

Speed of the Boat B while returning, s = 90 km/h

For Boat A round trip:

Time taken = 2 X d/s

                   = 2 X 60/ 60

                   = 2 hours

For Boat B round trip:

Time taken = 60/30 + 60/90

                   = 2 + 0.66 = 2.66 hours

Time taken by Boat A is less than by Boat B.

Time difference = 2.66 - 2.00 = 0.66 hrs = 40 min

Therefore, Boat A wins the race by 40 min.

(b)

Average speed of Boat A = 2 X l/2

                                            = 2 X 60/2

                                            = 60 km/hr

Therefore, average speed of Boat A is 60 km/hr.