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

$\displaystyle 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 $\displaystyle a,\;b,\;c,\;d\;$ and $\displaystyle \;e$

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

Can you please show working.

Thanks for your help