Between two bus stops

Wanda lives between two bus stops at three-eighths of their distance. He started the house today and found that he would have arrived at the bus stop if he had run to one or the other. The average bus speed is 60 km/h. What is Wanda's average running speed today?

Correct answer:

v =  15 km/h

Step-by-step explanation:

$$\begin{gathered} s_1=\frac{3}{8}s \\ {s}_2=s-s_1=\frac{5}{8}s \\ {v}_a=60\text{km/h} \\ {s}_1=v\cdot t_1 \\ {s}_2=v\cdot t_2 \\ {s}_3=v_a\cdot t_1 \\ {s}_3+s=v_a\cdot t_2 \\ {v}_a\cdot t_1+s=v_a\cdot t_2 \\ {v}_a\cdot s_1/v+s=v_a\cdot s_2/v \\ {v}_a\cdot \frac{3}{8}\cdot s/v+s=v_a\cdot \frac{5}{8}\cdot s/v \\ {v}_a\cdot \frac{3}{8}/v+1=v_a\cdot \frac{5}{8}/v \\ {v}_a\cdot \frac{3}{8}+v=v_a\cdot \frac{5}{8} \\ v=v_a\cdot \frac{5}{8}-v_a\cdot \frac{3}{8} \\ v=v_a\cdot (\frac{5}{8}-\frac{3}{8})=60\cdot (\frac{5}{8}-\frac{3}{8})=15\text{km/h} \end{gathered}$$

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