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Math Help - A man walks then runs...

  1. #1
    Senior Member Stroodle's Avatar
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    A man walks then runs...

    A man walks at a speed of 2 km/h for 45 minutes and then runs at 4 km/h for 30 minutes. Let S km be the distance the man has run after t minutes. The distance travelled can be described by:

    S(t)=\left\{\begin{array}{ll}at &\mbox{ if } 0\leq t\leq c\\bt+d, & \mbox{ if } c<t\leq e\end{array}\right.

    Find the values of a,\;b,\;c,\;d\; and \;e


    I can't get my head around this question. All I have so far is c=45 and e=75

    Can you please show working.
    Thanks for your help
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  2. #2
    Super Member
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    Quote Originally Posted by Stroodle View Post
    A man walks at a speed of 2 km/h for 45 minutes and then runs at 4 km/h for 30 minutes. Let S km be the distance the man has run after t minutes. The distance travelled can be described by:

    S(t)=\left\{\begin{array}{ll}at &\mbox{ if } 0\leq t\leq c\\bt+d, & \mbox{ if } c<t\leq e\end{array}\right.

    Find the values of a,\;b,\;c,\;d\; and \;e


    I can't get my head around this question. All I have so far is c=45 and e=75

    Can you please show working.
    Thanks for your help
    Remember: "distance equals rate times time", or d = rt.

    a is going to be the first speed. But it's 2 km/h, and t is supposed to be in minutes, so convert: 2 \;\text{km/h} = \frac{1}{30}\;\text{km/min} = a.

    The second speed is going to be 4 \;\text{km/h} = \frac{1}{15}\;\text{km/min} = b.

    Note that the speed changes after 45 minutes. We need to know the distance traveled: \left(\frac{1}{30}\;\text{km/min}\right)\times 45\;\text{min} = 1.5\;\text{km}.

    The equation find the distance after having run for 45 minutes @ 2 km/h would be
    \begin{aligned}<br />
\frac{1}{15}(t - 45) + 1.5 &= \frac{1}{15}t - 3 + 1.5 \\<br />
&= \frac{1}{15}t - 1.5 \\<br />
&= bt + d<br />
\end{aligned}

    so b = 1/15 and d = -1.5.


    Therefore,
    S(t)=\left\{\begin{array}{ll}\frac{1}{30}t &\mbox{ if } 0\leq t\leq 45\\\frac{1}{15}t-1.5, & \mbox{ if } 45<t\leq 75\end{array}\right.


    01
    Last edited by yeongil; June 20th 2009 at 05:18 AM. Reason: Fixed some errors
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  3. #3
    Senior Member Stroodle's Avatar
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    Haha. I just didn't notice that it was in minutes...
    I spent like 20 mins wondering why a wasn't 2
    Thanks!
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