Help me solve this

Question

Two boats start together and race across a 58-km-wide lake and back. Boat A goes across at 58 km/h and returns at 58 km/h. Boat B goes across at 29 km/h, and its crew, realizing how far behind it is getting, returns at 87 km/h. Turnaround times are negligible, and the boat that completes the round trip first wins.

Which boat wins Boat A or Boat B or is it a tie?

a) By how much?

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

Answer 1

Dear Dani,

We use the equation of time equal distance divided by velocity, t=d/v.

Let t_1a be the time boat 1 took to cross the lake and t_2a be the return time. We find

t_1total = t_1a+t_2a=58/58 + 58/58 = 2hours.

For the second boat

t_2total = t_1b+t_2b=58/29 + 58/87 = 2.667 hours.

The first boat won the race by 0.667 hours or 40 minutes.

The average velocity of the winning boat is simply 58 km/h

I hope it helps.