Cycling trip

At 8:00 AM, a group of children from a summer camp set off on a cycling day trip. After 9:00, the weather deteriorated sharply and the leader decided to send a bus along the same route to pick up the children. The bus departed at 10:00. When and at what distance from the camp did the bus catch up with the children, if the children cycled at an average speed of 15 km/h and the bus travelled at 75 km/h?

Final Answer:

t =  0.5 h
s =  37.5 km

Step-by-step explanation:

$$\begin{gathered} v_1=15\text{km/h} \\ {v}_2=75\text{km/h} \\ {s}_1=s_2 \\ {v}_1\cdot (t+(10-8))=v_2\cdot t \\ 15\cdot (t+(10-8))=75\cdot t \\ 60t=30 \\ t=\frac{30}{60}=0.5 \\ t=\frac{1}{2}=0.5=0.5\text{h} \end{gathered}$$

$s=v_2\cdot t=75\cdot 0.5=37.5\text{km}$

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