Question

Two boats start together and race across a 48-km-wide lake and back. Boat A goes across at 48 km/h and returns at 48 km/h. Boat B goes across at 24 km/h, and its crew, realizing how far behind it is getting, returns at 72 km/h. Turnaround times are negligible, and the boat that completes the round trip first wins.

(1) Which boat wins? (Or is it a tie?)

(A) boat A
(B) boat B
(C) it's a tie
.
(2) By how much? answer in km
(3) What is the average velocity of the winning boat? answer needs to be km/h

Answer 1

Boat A wins the race since it takes a total of 2 hours for the round trip, which is faster than Boat B's 2.6667 hours. Boat A wins by approximately 48 km when Boat B finishes. The average velocity of the winning boat (Boat A) is 48 km/h.

Step-by-step explanation:

To determine which boat wins and by how much, we need to calculate the time each boat takes to make the round trip across the 48-km-wide lake. For Boat A, since it travels at 48 km/h both ways, the time to go across and back is simply the total distance (48 km there and 48 km back, for a total of 96 km) divided by the speed (48 km/h):

Time for Boat A = Total Distance / Speed = 96 km / 48 km/h = 2 hours.
For Boat B, the time to go across at 24 km/h and come back at 72 km/h must be calculated separately and then summed:

Time to go across for Boat B = Distance / Speed = 48 km / 24 km/h = 2 hours.
Time to come back for Boat B = Distance / Speed = 48 km / 72 km/h = 0.6667 hours.
Total time for Boat B = 2 hours + 0.6667 hours = 2.6667 hours.
Boat A wins since it takes less time to complete the round trip.

To find out by how much Boat A wins, we need to convert the time difference into distance. Since Boat A has already finished when Boat B has 0.6667 hours to go, we calculate how far Boat B would travel in that time at their average speed on the way back (72 km/h):

Difference in distance = Time difference x Speed of Boat B on return = 0.6667 hours x 72 km/h = 48 km.
For the average velocity of the winning boat (Boat A), considering the round trip without any rest or waiting time, it remains constant at 48 km/h because it travels at that speed in both the outward and return journeys.

Answer 2

Part 1)

Boat A will win the race

Part 2)

Boat A will win the race by 48 km as the 2nd boat will reach the other end while boat A will just touches the finish line

Part 3)

average velocity must be zero

Step-by-step explanation:

As we know that the distance moved by the boat is given as

`d = 48 km`

now the time taken by the boat to move to and fro is given as

`t = (d)/(v)`

`t = (48 + 48)/(48)`

`t = 2 hrs`

Time taken by Boat B to cover the distance

`t = (48)/(24) + (48)/(72)`

`t = 2.66 h`

Part 1)

Boat A will win the race

Part 2)

Boat A will win the race by 48 km as the 2nd boat will reach the other end while boat A will just touches the finish line

Part 3)

Since the displacement of Boat A is zero

so average velocity must be zero