Runners

If John has a running speed of 3.5 miles per hour and Lucy has a speed of 5 miles per hour. If John starts running at 10:00 AM and Lucy starts running at 10:30 AM, what time will they meet? (as soon as possible)

Result

t = 11:40 hh:mm

Step-by-step explanation:

$$\begin{gathered} v_1=3.5\text{mph} \\ {v}_2=5\text{mph} \\ {t}_2=10+30/60=\frac{21}{2}=10.5\text{h} \\ {s}_1=s_2 \\ {v}_1\cdot (t-10.00)=v_2\cdot (t-t_2) \\ 3.5\cdot (t-10.00)=5\cdot (t-10.5) \\ 1.5t=17.5 \\ t=\frac{17.5}{1.5}=11.66666667 \\ t=\frac{35}{3}\doteq 11.666667=11.66667=11:40\text{hh}:\text{mm} \end{gathered}$$

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