Athletic oval

On the 400 m athletic oval, two athletes started back to back from the same level. After the starting shot, they both ran away from each other simultaneously. Athlete A ran at 15 km/h, and Athlete B ran at 17 km/h. A) in how many seconds did the athletes meet each other? B) how many meters did each athlete run before they met?

Correct answer:

t =  45 s
s₁ =  187.5 m
s₂ =  212.5 m

Step-by-step explanation:

$$\begin{gathered} s=400\text{m} \\ {v}_1=15\text{km/h}\to \text{m/s}=15:3.6\text{m/s}=4.16667\text{m/s} \\ {v}_2=17\text{km/h}\to \text{m/s}=17:3.6\text{m/s}=4.72222\text{m/s} \\ t=\frac{s}{v_1+v_2}=\frac{400}{\frac{25}{6}+\frac{85}{18}}=45\text{s} \end{gathered}$$

$s_1=v_1\cdot t=\frac{25}{6}\cdot 45=\frac{25\cdot 45}{6}=\frac{1125}{6}=187.5\text{m}$

$s_2=v_2\cdot t=\frac{85}{18}\cdot 45=\frac{85\cdot 45}{18}=\frac{3825}{18}=212.5\text{m}$

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