Grandmother's 82432

Filip traveled 15 km from Monika's house to his grandmother's village.
Monika can visit him. They meet at the point where the bikes arrive. They both left the house at 9:00.
At what time did they meet when Philip was walking at a speed of 19 km/h and Monika at a speed of 15 km/h?
How many km did Monika have to drive to meet?

Result

t = 9:26 hh:mm
s₂ =  6.6176 km

Step-by-step explanation:

$$\begin{gathered} s=15\text{km} \\ {v}_1=19\text{km/h} \\ {v}_2=15\text{km/h} \\ {s}_1+s_2=s \\ {v}_1\cdot (t-9.00)+v_2\cdot (t-9.00)=s \\ {v}_1\cdot T+v_2\cdot T=s \\ 19\cdot T+15\cdot T=15 \\ 34T=15 \\ T=\frac{15}{34}=0.44117647 \\ T=\frac{15}{34}\doteq 0.441176 \\ t=T+9.00=0.4412+9.00=9.44118=9:26\text{hh}:\text{mm} \end{gathered}$$

$$\begin{gathered} s_1=v_1\cdot T=19\cdot 0.4412=\frac{285}{34}\doteq 8.3824\text{km} \\ {s}_2=v_2\cdot T=15\cdot 0.4412=\frac{225}{34}\doteq 6.6176\text{km} \\ \text{ Verifying Solution: } \\ {s}_3=s_1+s_2=8.3824+6.6176=15\text{km} \end{gathered}$$

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