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Math Help - Find the Speed

  1. #1
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    Find the Speed

    During the first part of a trip, a canoeist travels 37 miles at a certain speed. The canoeist travels 7 miles on the second part or the trip at a speed 5 mph slower. The total time for the trip is 4 hours. What is the speed on each part of the trip?
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  2. #2
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    Hello, magentarita!

    During the first part of a trip, a canoeist travels 37 miles at a certain speed.
    The canoeist travels 7 miles on the second part or the trip at a speed 5 mph slower.
    The total time for the trip is 4 hours.
    What is the speed on each part of the trip?
    We will use: . \text{Time} \:=\:\frac{\text{Distance}}{\text{Speed}}

    Let r = speed on the first part.
    Then r - 5 = speed on the second part.

    He went 37 miles at r mph.
    . . This took: . \frac{37}{r} hours.

    He went 7 miles at r-5 mph.
    . . This took: . \frac{7}{r-5} hours.

    His total time was 4 hours: . \frac{37}{r} + \frac{7}{r-5} \:=\:4

    Now solve for r . . .



    Warning: We get a quadratic that doesn't factor.
    . . . . . . .Use the Quadratic Formula and approximate the answer.
    .
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  3. #3
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    ok............

    Quote Originally Posted by Soroban View Post
    Hello, magentarita!

    We will use: . \text{Time} \:=\:\frac{\text{Distance}}{\text{Speed}}

    Let r = speed on the first part.
    Then r - 5 = speed on the second part.

    He went 37 miles at r mph.
    . . This took: . \frac{37}{r} hours.

    He went 7 miles at r-5 mph.
    . . This took: . \frac{7}{r-5} hours.

    His total time was 4 hours: . \frac{37}{r} + \frac{7}{r-5} \:=\:4

    Now solve for r . . .


    Warning: We get a quadratic that doesn't factor.
    . . . . . . .Use the Quadratic Formula and approximate the answer.
    .
    Thanks for your reply and the tip at the end.
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