Average speed 4

Starting at home Tony traveled uphill to the store for 45 minutes at 8 miles per hour. he then traveled back home on the same path at a speed of 24 miles per hour. what is his average speed for the entire trip?

Correct result:

v =  12 mph

Solution:

$$\begin{gathered} t_1=45\mathrm{/}60={\displaystyle \frac{3}{4}}=0.75\text{ h } \\ {v}_1=8\text{ mph } \\ {v}_2=24\text{ mph } \\ s=v_1\cdot t_1=8\cdot 0.75=6\text{ km } \\ {t}_2=s\mathrm{/}{v}_2=6\mathrm{/}24={\displaystyle \frac{1}{4}}=0.25\text{ h } \\ v=2\cdot s\mathrm{/}(t_1+t_2)=2\cdot 6\mathrm{/}(0.75+0.25)=12\text{ mph} \end{gathered}$$

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