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1D Kinematics : Speed & Distance

  1. May 24, 2007 #1
    1. The problem statement, all variables and given/known data

    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)?

    2. Relevant equations


    Average Speed = Total distance/total time

    3. 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??
  2. jcsd
  3. May 24, 2007 #2
    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.
  4. May 24, 2007 #3
    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?
  5. May 24, 2007 #4
    Where is boat B when boat A wins the race?
  6. May 24, 2007 #5
    I'm sorry I am still confused
  7. May 24, 2007 #6


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    Homework Helper

    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?
  8. May 24, 2007 #7
    42 km right because when boat A finishes the race in 2hours boat b has traveled 42 km.

    42km/21km/hr = 2h

  9. May 24, 2007 #8


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    Homework Helper

    Sounds good to me.
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