Bus stop

Find at what time the bus leaves from the bus stop outside the village. If you know that when you leave home at 8:00 and go at a speed of 3 km/h, you come to a stop 9 minutes after the departure of the bus, and when you go at a speed of 4 km/h, you come to the bus stop 10 minutes before departure. Calculate the distance from the village to the bus stop.

Result

t = 9:07 hh:mm
s =  3.8 km

Step-by-step explanation:

$$\begin{gathered} v_1=3\text{km/h} \\ {v}_2=4\text{km/h} \\ \Delta t_1=9\text{min}\to \text{h}=9:60\text{h}=0.15\text{h} \\ \Delta t_2=10\text{min}\to \text{h}=10:60\text{h}=0.16667\text{h} \\ s=v_1\cdot (x+\Delta t_1) \\ s=v_2\cdot (x-\Delta t_2) \\ {v}_1\cdot (x+\Delta t_1)=v_2\cdot (x-\Delta t_2) \\ 3\cdot (x+0.15)=4\cdot (x-0.16666666666667) \\ x=1.116667 \\ x=\frac{1.11666667}{1}=1.11666667 \\ x=\frac{67}{60}\doteq 1.116667 \\ t=8.00+x=8.00+1.1167=9.11667=9:07\text{hh}:\text{mm} \end{gathered}$$

$s=v_1\cdot (x+\Delta t_1)=3\cdot (1.1167+0.15)=3.8\text{km}$

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