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A pedestrian leaves point A at a speed of v₁ = 5 km/h.
After 3 hours, a cyclist sets off from the same place at a speed of v₂ = 20 km/h.
At the same time as the cyclist, a car starts from point B, which is 50 km away.
Calculate the distance and time at which the cyclist overtakes the pedestrian, and find the speed v at which the car must travel for all three to meet at the same point and time.

Final Answer:

s =  20 km
t =  1 h
v =  70 km/h

Step-by-step explanation:

$$\begin{gathered} v_1=5\text{km/h} \\ {v}_2=20\text{km/h} \\ {s}_1=50\text{km} \\ {t}_1=3\text{h} \\ s=v_1\cdot (t+t_1) \\ s=v_2\cdot t \\ s=5\cdot (t+3) \\ s=20\cdot t \\ s-5t=15 \\ s-20t=0 \\ Row2-Row1\to Row2 \\ -15t=-15 \\ t=\frac{-15}{-15}=1 \\ s=15+5t=15+5\cdot 1=20 \\ s=20 \\ t=1 \end{gathered}$$

$$\begin{gathered} s+s_1=v\cdot t \\ 20+50=v\cdot 1 \\ v=70=70\text{km/h} \end{gathered}$$

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