Intervals 12201

Trams of five lines run at intervals of 5, 8, 10, 12, and 15 minutes. At noon, they left the station at the same time. What time will they meet again? How many times will each tram pass the stop during that time?

Correct answer:

s =  14 hh:mm
a =  24
b =  15
c =  12
d =  10
e =  8

Step-by-step explanation:

$$\begin{gathered} 5...\text{ prime number} \\ 8=2^3 \\ 10=2\cdot 5 \\ 12=2^2\cdot 3 \\ 15=3\cdot 5 \\ LCM(5,8,10,12,15)=2^3\cdot 3\cdot 5=120 \\ m=LCM(5,8,10,12,15)=120\text{min} \\ t=m\to \text{h}=m:60\text{h}=120:60\text{h}=2\text{h} \\ s=12.00+t=12.00+2=14\text{hh}:\text{mm} \end{gathered}$$

$a=m/5=120/5=24$

$b=m/8=120/8=15$

$c=m/10=120/10=12$

$d=m/12=120/12=10$

$e=m/15=120/15=8$

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