Bike departure time

Wes is supposed to be at the playground, 2.5 km away from his home, in 15 hours and 30 minutes. If he drives at 50 km/h, what time does he have to ride his bike to be on the field 5 minutes earlier?

Result

t = 15:22 hh:mm

Step-by-step explanation:

$$\begin{gathered} t_1=15+30/60=\frac{31}{2}=15.5\text{h} \\ {t}_2=\frac{5}{60}=\frac{1}{12}\doteq 0.0833\text{h} \\ s=2.5\text{km} \\ v=50\text{km/h} \\ {t}_3=s/v=2.5/50=\frac{1}{20}=0.05\text{h} \\ t=t_1-t_2-t_3=\frac{31}{2}-\frac{1}{12}-\frac{1}{20}=\frac{930}{60}-\frac{5}{60}-\frac{3}{60}=\frac{930-5-3}{60}=\frac{922}{60}=15.36667=15:22\text{hh}:\text{mm} \end{gathered}$$

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