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Math Help - word problems

  1. #1
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    word problems

    a man drives 108 km at an average rate. If he had driven 5km/hr. faster, he would have made the trip in 15 hours less time. How fast did he drive?
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  2. #2
    Junior Member
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    Word Problem

    You know that  Time = \frac {Distance}{Speed}.

    Distance = 108 km

    Speed  = s km/h

    If he had driven  5 km/hr faster, he would have reached in 15 hours less time.

    That means... Actual Time taken - Time taken while driving 5 km/h faster  = 15 hours.

    \Rightarrow \frac {108}{s} - \frac {108}{s + 5} = 15

    Now express as a single fraction:

    \Rightarrow \frac {108 (s + 5) - 108s}{s (s + 5)} = 15

    Now multiply both sides by the denominator, s (s + 5).

    \Rightarrow 108 (s + 5) - 108s = 15s (s + 5)

    \Rightarrow 108s + 540 - 108s = 15s^2 + 75s

    \Rightarrow 540 = 15s^2 + 75s

    \Rightarrow 15s^2 + 75s - 540 = 0

    Divide throughout by 15:

    \Rightarrow s^2 + 5s - 36 = 0

    Now factorise:

    \Rightarrow (s + 9) (s - 4) = 0

    \Rightarrow Either  s = -9(discard) or s = 4 .

    Check: So he was driving at 4 km/h.

    Time taken to drive at 4 km/h  = \frac {108}{4} = 27 hours.

    Time taken to drive at 9 km/h  = \frac {108}{9} = 12 hours.

    Difference in times  = 27 - 12 = 15 hours.

    at above poster.

    I hope that helps.

    ILoveMaths07.
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