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25 April, 19:06

Two boats start together and race across a 74-km-wide lake and back. Boat A goes across at 74 km/h and returns at 74 km/h. Boat B goes across at 37 km/h, and its crew, realizing how far behind it is getting, returns at 111 km/h. Turn around times are negligible, and the boat that completes the round trip first wins ...

a) Which boat wins? (or is it a tie?)

b) By how much? ... km

c) What is the average velocity of the winning boat? ... km/h

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  1. 25 April, 19:30
    0
    74 Km/h

    Explanation:

    For boat A:

    1 = 2l/v_1

    =2*74/74 h

    =2h

    where = 74 wide of the lake, 1 - speed of boat A

    For boat B:

    2 = l/v_21 + l/v_22

    = 74/37 + 74/111 ℎ

    = 2.66 ℎ

    where v_21 = 37 / ℎ and v_22 = 111 / ℎ speeds of boat B

    boat A completes the round trip first. The difference of times equals:

    ∆ = 2 - 1

    =2.66 ℎ - 2ℎ

    =0.66 ℎ or 40 n

    boat A, ∆ = 40 n

    c) Average speed for boat A equals:

    V = 2 / 1

    =148/2 Km/h

    =74 Km/h
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