math(rational functions application)

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The average speed of a jet is 100km/h faster than a cargo plane. To travel 1400km, the cargo plane requires 25% more time than the jet. Find the average speed of the jet.

This is the formula I figured out so far.

V(average)=V(jet)-V(cargo
100km/h= d/t - d/t
100= [1400km/x] - [1400/(.25x+x)]

But from here I don't know what to do..

  • math(rational functions application) -

    Call the speeds j and c.

    j - c = 100 -> j = 100 + c

    (100 + c) = 5c / 4 (from the "25% faster")

    Solve for c.

  • math(rational functions application) -

    Creating a chart makes these kind of problems real easy

    3 columns: Distance, Rate , Time and remember D = RT
    2 rows: jet and cargo plane

    -----D-----R------T
    Jet 1400 -- x+100 -- 1400/(x+100)
    Cargo 1400 ----x -- 1400/x

    (hope the spacing comes out halfdecent.)

    It said the time of the cargo plane is 25% more than the time of the jet, so
    1400/x = 1.25(1400)/(x+100)
    1400/x = 1750/(x+100)
    cross-multiply
    1750x = 1400x + 140000
    x = 400

    So the cargo's speed is 400 km/h and the jet goes 500 km/h

    check:
    time of jet = 1400/500 = 2.8 hours
    time of cargo = 1400/400 = 3.5

    What is 25% of 2.8 added to 2.8 ?
    YUP!!!!

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