1D Kinematics : Speed & Distance

[toothpick09]

Homework Statement

Two boats start together and race across a 42 km wide lake and back. Boat A goes across at 42 km/h and returns at 42 km/h. Boat B goes across at 21 km/h, and its crew, realizing how far behind it is getting, returns at 63 km/h. Turnaround times are negligible, and the boat that completes the round-trip first wins.

Which boat wins and by how much(km)?

Homework Equations

Conversions

Average Speed = Total distance/total time

The Attempt at a Solution

I took 42km/h * 1h/84km = 1/2h for boat A to travel there and 1/2 h to travel back.

21km/h * 1h/84km = 1/4h for boat B to travel there leaving it 3/4h to travel back.

Next I took the speed and multiplied by the hours:
42km/h * 1/4h = 10.5 km
21km/h * 1/4h = 5.25 km
63km/h * 3/4h = 47.25 km

Then added the distance of boat B and subtracted boat A:
(47.25km + 5.25km) - (10.5km + 10.5km) = 31.5km

What am I doing wrong??

 

[neutrino]

Given this: Average Speed = Total distance/total time

The time taken would be equal to Total distance/Avg. speed

Now, calculate the time it would take boat A to cross the lake once, and then do the same for it's return trip.

 

[toothpick09]

So ...

42km/42km/h = 1h which means 2h there and crossing the finish line for boat A

for boat B: 42km/21km/h = 2h and 42km/63km/h = 2/3h meaning 8/3 hour for boat B's trip to and fro.

but that is just the time it takes them to make the trip how do you find the distance?

 

[neutrino]

but that is just the time it takes them to make the trip how do you find the distance?

Where is boat B when boat A wins the race?

 

[toothpick09]

I'm sorry I am still confused

 

[hage567]

You know how much time it took for Boat A to win the race. So at the time that Boat A finishes, how far has Boat B gone in the race at that point?

 

[toothpick09]

42 km right because when boat A finishes the race in 2hours boat b has traveled 42 km.

42km/21km/hr = 2h

?

 

[hage567]

Sounds good to me.