Cycling training time

Patricia got so excited about the cycling race that she started training every day. She notices that she travels 10 km in as many minutes as her average speed in kilometers per hour. Her last training route was 50 km. How long did it take her to cross it?

Final Answer:

t₂ =  2.0412 h

Step-by-step explanation:

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

Try another example