Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

Math problem?

A boat takes 1hr longer to go 36km up a river than to go down the river. If the boat travels 15km/hr in still water, what is the speed of the current?

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  • 1 month ago

    A boat takes 1 hr longer to go 36 km up a river than to go down the river. 

    If the boat travels 15 km/hr in still water, the speed of the current is 3 km/hr.

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  • (15 - r) * t = 36

    (15 + r) * (t - 1) = 36

    t = 36 / (15 - r)

    (15 + r) * (36 / (15 - r)  - 1)  =  36

    (15 + r) * ((36 - (15 - r)) / (15 - r) = 36

    (15 + r) * (36 - 15 + r) = 36 * (15 - r)

    (15 + r) * (21 + r) = 36 * (15 - r)

    315 + 15r + 21r + r^2 = 540 - 36r

    315 + 36r + r^2 = 540 - 36r

    r^2 + 36r + 36r + 315 - 540 = 0

    r^2 + 72r - 225 = 0

    r = (-72 +/- sqrt(72^2 - 4 * 1 * (-225))) / 2

    r = (-72 +/- sqrt(4 * 36^2 + 4 * 225)) / 2

    r = (-72 +/- 2 * sqrt(36^2 + 15^2)) / 2

    r = -36 +/- sqrt(3^2 * 12^2 + 3^2 * 5^2)

    r = -36 +/- 3 * sqrt(12^2 + 5^2)

    r = -36 +/- 3 * sqrt(169)

    r = -36 +/- 3 * 13

    r = -36 +/- 39

    r = -75 , 3

    r > 0

    r = 3

    The river is flowing at 3 km/hr

    15 + 3 = 18

    18 * 2 = 36

    15 - 3 = 12

    12 * 3 = 36

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