Directions 70274

Two runners train on a circular track that is 375 m long. When they start from the same place and run in opposite directions, they meet in 30 seconds. When they run in the same direction, they are 15 m apart in 30 seconds. What is the average speed of each of the runners?

Correct answer:

v₁ =  6.5 m/s
v₂ =  6 m/s

Step-by-step explanation:

$$\begin{gathered} o=375\text{m} \\ {t}_1=30\text{s} \\ {t}_2=30\text{s} \\ {s}_2=15\text{m} \\ {v}_1\cdot t_1+v_2\cdot t_2=o \\ {v}_1\cdot t_2-v_2\cdot t_2=s_2 \\ {v}_1\cdot 30+v_2\cdot 30=375 \\ {v}_1\cdot 30-v_2\cdot 30=15 \\ 30v_1+30v_2=375 \\ 30v_1-30v_2=15 \\ Row2-Row1\to Row2 \\ 30v_1+30v_2=375 \\ -60v_2=-360 \\ {v}_2=\frac{-360}{-60}=6 \\ {v}_1=\frac{375-30v_2}{30}=\frac{375-30\cdot 6}{30}=6.5=6.5\text{m/s} \\ {v}_1=\frac{13}{2}=6.5 \\ {v}_2=6 \end{gathered}$$

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