Two friends

Two friends on a bicycle rode against each other from two places 49 km apart. The first set off at 8.00 at a speed of 20 km/h, the second 12 minutes later at a speed of 25 km/h. What time do they meet? How many km will each of them travel since then?

Result

t = 9:12 hh:mm
a =  24 km
b =  25 km

Step-by-step explanation:

$$\begin{gathered} s=49\text{km} \\ {v}_1=20\text{km/h} \\ {v}_2=25\text{km/h} \\ {t}_1=8.00\text{h} \\ {t}_2=0:12=0hr12min=0+\frac{12}{60}=0.2hr=0.2 \\ a+b=s \\ a=v_1\cdot x \\ b=v_2\cdot (x-t_2) \\ {v}_1\cdot x+v_2\cdot (x-t_2)=s \\ 20\cdot x+25\cdot (x-0.2)=49 \\ 45x=54 \\ x=\frac{54}{45}=1.2 \\ x=\frac{6}{5}=1.2 \\ t=t_1+x=8+1.2=9.2=9:12\text{hh}:\text{mm} \end{gathered}$$

$a=v_1\cdot x=20\cdot 1.2=24\text{km}$

$b=v_2\cdot (x-t_2)=25\cdot (1.2-0.2)=25\text{km}$

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