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Thread: 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
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    Word Problem

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

    Distance $\displaystyle = 108 $ km

    Speed $\displaystyle = s$ km/h

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

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

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

    Now express as a single fraction:

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

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

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

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

    $\displaystyle \Rightarrow 540 = 15s^2 + 75s $

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

    Divide throughout by $\displaystyle 15$:

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

    Now factorise:

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

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

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

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

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

    Difference in times $\displaystyle = 27 - 12 = 15 $ hours.

    at above poster.

    I hope that helps.

    ILoveMaths07.
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