? asked in Science & MathematicsMathematics · 1 decade ago

Several precalculus word problems...I need help!?

1. Current of river = 2miles/h. A boat travels 8 miles upstream and back in 3 hours. What is the speed of boat in still water? I know that the answer is 6, logically, but when I tried solving this using formula, I got 6.122. What is the proper formula to solve this problem?

2. A water tank can be filled by an inlet pipe in 8 hours. It takes twice that long for the outlet pipe to empty the tank. How long will it take to fill the tank if both pipes are open? What is the formula; I know that the answer is 16, logically.

3. Find two consecutive even integers, the sum of whose reciprocals is 3/4.

Thank you guys.

Update:

you're a genius TC thank you

1 Answer

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  • 1 decade ago
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    1. let x = rate in still water of the boat...

    upstream: rate = (x-2) ... distance = 8 ... time = 8/(x-2)

    downstream: rate = (x+2) ... distance = 8 ... time = 8/(x+2)

    the total time = 3 = 8/(x-2) + 8/(x+2)

    3 = [8(x+2) + 8(x-2)] / x^2 - 4 ... cross multiplying...

    3x^2 - 12 = 16x

    3x^2 - 16x - 12 = 0

    (3x + 2) (x - 6) = 0

    thus x = 6

    2. inlet: in one hour: 1/8

    outlet: in one hour: -1/16

    combined: in one hour: 1/8 - 1/16 = 1/16 of the tank

    thus it will take 16 hours...

    3. 1/x + 1/(x+2) = 3/4

    [(x+2) + x]/x^2 + 2x = 3/4

    4(2x+2) = 3(x^2+2x)

    8x + 8 = 3x^2 + 6x

    3x^2 - 2x - 8 = 0

    (3x + 4)(x - 2) = 0

    thus two numbers: 2 & 4.

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