Shortcut

The road from the cottage to the shop 6 km away leads either along a straight road that the bicycle can drive at a speed of 18 km/h or by "shortcut". It measures only 3.6 km. But the road from the cottage is all uphill - at a speed of 8 km/h, you can go home downhill at a safe speed of 24 km/h. The purchase takes the same time. Jana goes flat on Monday, Tomáš "shortcut" on Tuesday. Who will be back first?

Result

t₁ = 0:40 h
t₂ = 0:36 h

Step-by-step explanation:

$$\begin{gathered} s_1=6\text{km} \\ {v}_1=18\text{km/h} \\ {s}_2=3.6\text{km} \\ {v}_2=8\text{km/h} \\ {v}_3=24\text{km/h} \\ {t}_1=2\cdot s_1/v_1=2\cdot 6/18=\frac{2}{3}=0.66667=0:40\text{h} \end{gathered}$$

$$\begin{gathered} t_2=s_2/v_2+s_2/v_3=3.6/8+3.6/24=\frac{3}{5}=0.6=0:36\text{h} \\ {t}_1>t_2 \\ T \end{gathered}$$

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