Pavol 3

Pavol and Roman trained on a running track of length 400 m. At a certain moment they ran from the start in the same direction and ran at a uniform motion. When Pavol, after completing five laps in time 6 min 40 s, passed the starting point again, he overtook Roman, who had completed one lap fewer.
a) What large average speed did each boy run?
b) In what time did each boy run one lap?
c) What distance was Roman behind Pavol at the moment when Pavol completed the first lap?

Final Answer:

v₁ =  5 m/s
v₂ =  4 m/s
T₁ =  80 s
T₂ =  100 s
x =  80 m

Step-by-step explanation:

$$\begin{gathered} s=400\text{m} \\ {t}_5=6\cdot 60+40=400\text{s} \\ {n}_1=5 \\ {n}_2=n_1-1=5-1=4 \\ {s}_1=n_1\cdot s=5\cdot 400=2000\text{m} \\ {v}_1=\frac{s_1}{t_5}=\frac{2000}{400}=5\text{m/s} \end{gathered}$$

$$\begin{gathered} s_2=n_2\cdot s=4\cdot 400=1600\text{m} \\ {v}_2=\frac{s_2}{t_5}=\frac{1600}{400}=4\text{m/s} \end{gathered}$$

$T_1=t_5/n_1=400/5=80\text{s}$

$T_2=t_5/n_2=400/4=100\text{s}$

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