Cyclists

The cyclist who rides at an average speed 20 km/h travels a trip distance 13 min before the cyclist who rides at an average speed 15 km/h.

What is the length of this cyclist trip(distance in km)?

Correct answer:

s =  13 km

Step-by-step explanation:

$$\begin{gathered} v_1=20\text{km/h} \\ \Delta t=13\text{min}\to \text{h}=13:60\text{h}=0.21667\text{h} \\ {v}_2=15\text{km/h} \\ s=s_1=s_2 \\ {v}_1\cdot (t-\Delta t)=v_2\cdot t \\ 20\cdot (t-0.21666666666667)=15\cdot t \\ 5t=4.333333 \\ t=\frac{4.33333333}{5}=0.86666667 \\ t=\frac{13}{15}\doteq 0.866667 \\ s=v_1\cdot (t-\Delta t)=20\cdot (0.8667-0.2167)=13\text{km} \end{gathered}$$

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