Motorcycle and car

A car travels 11000 decimeters per minute, and a motorcycle travels at a speed of 330 meters in 11 seconds. They leave Prague from the same place, and the motorcycle leaves 45 minutes later behind the car. Who will be closer to Vimperek after an hour and a quarter of riding the motorcycle? By how many km?

Correct answer:

s =  3 km

Step-by-step explanation:

$$\begin{gathered} v_1=11000/10/60=\frac{55}{3}\doteq 18.3333\text{m/s} \\ {v}_2=330/11=30\text{m/s} \\ {t}_2=(1+1/4)\cdot 3600=4500\text{s} \\ {t}_1=t_2+45\cdot 60=4500+45\cdot 60=7200\text{s} \\ {s}_1=v_1\cdot t_1=18.3333\cdot 7200=132000\text{m} \\ {s}_2=v_2\cdot t_2=30\cdot 4500=135000\text{m} \\ s=|s_1-s_2|/1000=|132000-135000|/1000=3\text{km} \end{gathered}$$

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