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6 October, 23:16

David started across a lake 15 miles wide in his fishing boat at 10 miles per hour. He had to row the rest of the way at only 5 miles per hour after his motor went out. If he was rowing for half the time that the trip took, how long did the total trip take

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  1. 6 October, 23:26
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    Total time = 2hrs

    Step-by-step explanation:

    Firstly, to outline some variables, with which we can construct some equations:

    x = the time taken to cross the river at 10mph (in hrs)

    y = the time taken to cross the river at 5mph (in hrs)

    t = total time taken to cross the river (in hrs)

    a = distance travelled at speed 10mph (in miles)

    b = distance travelled at speed 5mph (in miles)

    Then,

    a + b = 15

    t = x + y

    y = ¹/₂ (t) ∴ t = 2y, so,

    x + y = 2y ∴ x = y

    Secondly, we know speed = distance/time, so,

    10 = a/x ⇒ x = a/10

    5 = b/x ⇒ x = b/5

    So,

    a/10 = b/5 ∴ a = 2b

    Thirdly, if a + b = 15, then,

    2b + b = 15 ⇒ 3b = 15 ⇒ b = 5

    [a = 2b ∴ a = 10]

    Fourthly, x = b/5, so,

    x = 5/5 = 1,

    Since x = y, y = 1 and since t = 2y,

    t = 2 (1) = 2

    The whole trip, therefore, took 2hrs.
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