Tractor

A car traveling at a speed of 70km/h is overtaken by a tractor traveling at 25km/h. The driver of the car needs a toilet and knows that it will take him 3 minutes. How many kilometers does the car have to cover, so the tractor does not overtake it?

Correct answer:

s =  1.9444 km

Step-by-step explanation:

$$\begin{gathered} v_1=70\text{km/h} \\ {v}_2=25\text{km/h} \\ t=3\text{min}\to \text{h}=3:60\text{h}=0.05\text{h} \\ {s}_1=s_2 \\ {v}_2\cdot (x+t)=v_1\cdot x \\ 25\cdot (x+0.05)=70\cdot x \\ 45x=1.25 \\ x=\frac{1.25}{45}=0.02777778 \\ x=\frac{1}{36}\doteq 0.027778 \\ {s}_1=v_2\cdot (x+t)=25\cdot (0.0278+0.05)=\frac{35}{18}\doteq 1.9444\text{km} \\ {s}_2=v_1\cdot x=70\cdot 0.0278=\frac{35}{18}\doteq 1.9444\text{km} \\ s=s_1=1.9444=1.9444\text{km} \end{gathered}$$

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