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Math Help - Fractional Equations?

  1. #1
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    Fractional Equations?

    1) An intake pipe can fill a certain tank in 6 hours when the outlet pipe is closed, but with the outlet pipe open it takes 9 hours. How long would it take the outlet pipe to fill an empty tank?

    2) Members of the ski club contributed equally to obtain $1800 for a holiday trip. When 6 members found that they could not go, their contributions were refunded and each remaining member then had to pay $10 more to raise the $1800. How many went on the trip?

    3) Because of traffic Maria could average only 40 km/h for the first 20% of her trip, but she averaged 75 km/h for the whole trip. What was her average speed for the last 80% of her trip?

    4) A number x is the harmonic mean of a and b if 1/x is the average of 1/a and 1/b. Find two positive numbers that differ by 12 and have harmonic mean 5

    I don't know how to do these please help??
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  2. #2
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    Hello, Dunit0001!

    Here's #3 . . .


    3) Because of traffic Maria could average only 40 km/h for the first 20% of her trip.
    But she averaged 75 km/h for the whole trip.
    What was her average speed for the last 80% of her trip?

    We know that: . \text{Distance }\:=\:\text{Speed} \times \text{Time}

    . . and its variations: . \text{Time} \:=\:\frac{\text{Distance}}{\text{Speed}}\qquad\te  xt{Speed} \:=\:\frac{\text{Distance}}{\text{Time}}

    Suppose the trip was 400 km long.
    The first 20% is 80 km; the last 80% is 320 km.

    She drove 80 km at 40 kph.
    . . This took her: . \frac{80\text{ km}}{40\text{ kph}} \:=\:2 hours.

    The she drove 320 km at x kph.
    . . This took her: . \frac{320}{x} hours.

    Then, to drive 400 km, her total time was: . 2 + \frac{320}{x} hours.

    Hence, her average speed was: . \frac{400}{2 + \frac{320}{x}} kph.

    Since her average speed was 75 kph, we have: . \frac{400}{2 + \frac{320}{x}} \:=\:75

    . . Now solve for x.

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