Tram stop

At the tram stop met tram No. 4 and no. 5 at 10 AM. Tram no. 4 runs every 5 minutes, tram No. 5 at an interval of 7 minutes. How many times will meet until 12 o'clock?

Correct answer:

n =  3

Step-by-step explanation:

$$\begin{gathered} t_1=10.00 \\ {t}_2=12.00 \\ t=t_2-t_1=12-10=2\text{ h } \\ m=t\to \text{ min}=t\cdot 60\text{ min}=2\cdot 60\text{ min}=120\text{ min } \\ {T}_1=5\text{ min } \\ {T}_2=7\text{ min } \\ 5\mathrm{.}\mathrm{.}\mathrm{.}\text{ prime number } \\ 7\mathrm{.}\mathrm{.}\mathrm{.}\text{ prime number } \\ LCM(5,7)=5\cdot 7=35 \\ T=LCM(T_1,T_2)=LCM(5,7)=35\text{ min } \\ {n}_0=m\mathrm{/}T=120\mathrm{/}35={\displaystyle \frac{24}{7}}=3\frac{3}{7}\doteq 3.4286 \\ n=\lfloor n_0\rfloor =\lfloor 3.4286\rfloor =3 \end{gathered}$$

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