Kilometers 9941

Petra got so excited about the cycling race that he started training every day. He notices that he travels 10 km in as many minutes as his average speed in kilometers per hour. His last training route was 50km. How long did it take him to cross it?

Correct answer:

t₂ =  2.0412 h

Step-by-step explanation:

$$\begin{gathered} s_2=50\text{km} \\ {s}_1=10\text{km} \\ {t}_1(min)=v(km/h) \\ {s}_1=v{t}_1 \\ {s}_1=v\cdot v/60 \\ v=\sqrt{s_1\cdot 60}=\sqrt{10\cdot 60}=10\sqrt{6}\text{km/h}\doteq 24.4949\text{km/h} \\ {t}_1=s_1/v=10/24.4949\doteq 0.4082\text{h} \\ {t}_{11}=t_1\to \text{min}=t_1\cdot 60\text{min}=0.4082\cdot 60\text{min}=24.4949\text{min} \\ {s}_{11}=v\cdot t_1=24.4949\cdot 0.4082=10\text{km} \\ {s}_{11}=s_1 \\ {t}_2=s_2/v=50/24.4949=2.0412\text{h} \end{gathered}$$

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