Per shift

Two cars take beets from the same field to the sugar factory. Both drive at the same average speed. A car with mechanical tipping needs 15 minutes to travel to the sugar factory and back. A car that does not have mechanical tipping needs 6 minutes longer for the same trip. Both cars leave at the same time in the morning. How often do they meet in the field per shift (8 hours)?

Correct answer:

n =  4

Step-by-step explanation:

$$\begin{gathered} t_1=15\text{min} \\ {t}_2=t_1+6=15+6=21\text{min} \\ s=8\text{h}\to \text{min}=8\cdot 60\text{min}=480\text{min} \\ 15=3\cdot 5 \\ 21=3\cdot 7 \\ LCM(15,21)=3\cdot 5\cdot 7=105 \\ T=LCM(t_1,t_2)=LCM(15,21)=105\text{min} \\ {n}_1=s/T=480/105=\frac{32}{7}=4\frac{4}{7}\doteq 4.5714 \\ n=\lfloor n_1\rfloor =\lfloor 4.5714\rfloor =4 \end{gathered}$$

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