Perpendicular roads

Two roads meet at a right angle. On one road there is place P at 5 km from the intersection, on the other road there is place R at 12 km from the intersection. Places P and R are connected by a direct path. A pedestrian goes from place R to place P along the path at an average speed of 5 km/h, a car goes from place R to P along the roads at an average speed of 60 km/h. Determine, how long after the arrival of the car in place P the pedestrian will arrive, if the car and the pedestrian set off from place R at the same time.

Result

t = 2:19 h

Step-by-step explanation:

$$\begin{gathered} a=5\text{km} \\ b=12\text{km} \\ {c}^2=a^2+b^2 \\ c=\sqrt{a^2+b^2}=\sqrt{5^2+12^2}=13\text{km} \\ {v}_1=5\text{km/h} \\ {v}_2=60\text{km/h} \\ {t}_1=c/v_1=13/5=\frac{13}{5}=2.6\text{h} \\ {t}_2=\frac{a+b}{v_2}=\frac{5+12}{60}=\frac{17}{60}\doteq 0.2833\text{h} \\ t=t_1-t_2=2.6-0.2833=2.31667=2:19\text{h} \end{gathered}$$

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