Question

A.   Garen observed his athletic friends, Aya and Marisa, run. The two girls ran in a 1.5-km straight dirt road. Marisa was a given a ten-second head-start. When Aya ran, she caught up with Marisa, who ran at 3.75 m/s. Both of them finished the 1000 m run, with Aya measured to finish the track at 375 seconds. (5 items x 5 points)

2.   How far did Marisa run after ten seconds? 3.75m/s

3.   Find the time Aya caught up alongside Marisa.

4.   Find the distance where both runners met.

5.   How long did Marisa run before she could finish the sprint?

Answer 1

2. 10 seconds at 3.75 m/s give us 37.5 m.

3. Speed of Aya: 1500 m/375 s=4 m/s. The time it took is

$$v_M(t+10)=v_At,\\\space\\ t=\frac{10v_M}{v_A-v_M}=150\text{ s}.$$

4. The distance is

$$d=v_M(t+10)=v_At=600\text{ m}.$$

5. The time is

$$t_M=1500/3.75=400\text{ s}.$$