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Math Help - Algebra speed problem

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    Exclamation Algebra speed problem

    It took a cyclist 6 h to travel 48 mi going against the wind. The next day on the return trip, it took the cyclist 3 h traveling with the wind. What was the speed of the cyclist?

    Also they say i need to make some chart so if you know of any charts to solve this problem please post them.
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  2. #2
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    Quote Originally Posted by sp0rtskid55 View Post
    It took a cyclist 6 h to travel 48 mi going against the wind. The next day on the return trip, it took the cyclist 3 h traveling with the wind. What was the speed of the cyclist?

    Also they say i need to make some chart so if you know of any charts to solve this problem please post them.
    Say the speed of the wind is V (in mph). If the cyclist's speed without the wind is v (in mph), then we know that the cyclist's speed with the wind is v + V and against it is v - V. So
    v - V = \frac{48}{6} = 8

    and
    v + V = \frac{48}{3} = 16

    Solving the bottom equation for V:
    V = 16 - v

    and inserting this value of V into the top equation:
    v - (16 - v) = 8

    2v - 16 = 8

    v = 12~mph

    -Dan
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