The cyclist

A cyclist travelled from a village to a town. The first half of the journey was at 24 km/h. The second half, which was mostly downhill, was at 38 km/h. The entire journey took 94 minutes. Calculate the distance from the village to the town.

Final Answer:

d =  46.0903 km

Step-by-step explanation:

$$\begin{gathered} v_1=24\text{km/h} \\ {v}_2=38\text{km/h} \\ T=94\text{min}\to \text{h}=94:60\text{h}=1.56667\text{h} \\ {v}_1\cdot t_1=v_2\cdot t_2 \\ {v}_1\cdot t_1=v_2\cdot (T-t_1) \\ 24\cdot t_1=38\cdot (1.5666666666667-t_1) \\ 62t_1=59.533333 \\ {t}_1=\frac{59.53333333}{62}=0.96021505 \\ {t}_1=\frac{893}{930}\doteq 0.960215 \\ {t}_2=T-t_1=1.5667-0.9602=\frac{94}{155}\doteq 0.6065\text{h} \\ {s}_1=v_1\cdot t_1=24\cdot 0.9602=\frac{3572}{155}\doteq 23.0452\text{km} \\ {s}_2=v_2\cdot t_2=38\cdot 0.6065=\frac{3572}{155}\doteq 23.0452\text{km} \\ d=s_1+s_2=23.0452+23.0452=46.0903\text{km} \end{gathered}$$

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