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. (a) which boat wins? (or is it a tie?)

Answer 1

Time required by boat 1 for the round trip is less than that of boat 2.

Hence, boat 1 wins.

Step-by-step explanation:

Case 1: Boat 1

Speed of boat =
`(distance of river)/(time)`

time =
`(distance of river)/(speed of boat)`

While going to another end

time =
`(distance of river)/(speed of boat)`

time =
`(48)/(48)`

time = 1 hour

While going back,

time =
`(distance of river)/(speed of boat)`

time =
`(48)/(48)`

time = 1 hour

Total time taken by boat 1 is,

Total time by boat 1 = 1 hour + 1 hour = 2 hour

Total time by boat 1 = 2 hour

Total time taken by boat 1 for the round trip is 2 hour.

Case 2: Boat 2

Speed of boat =
`(distance of river)/(time)`

time =
`(distance of river)/(speed of boat)`

While going to another end

time =
`(distance of river)/(speed of boat)`

time =
`(48)/(24)`

time = 2 hour

While going back,

time =
`(distance of river)/(speed of boat)`

time =
`(48)/(72)`

time = 0.66 hour

Total time taken by boat 2 is,

Total time by boat 1 = 2 hour + 0.66 hour

Total time by boat 1 = 2.66 hour

Total time taken by boat 2 for the round trip is 2.66 hour.

Time required by boat 1 for the round trip is less than that of boat 2.

Hence, boat 1 wins.