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:

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

Try another example

Related math problems and questions:

• Buses
  At the bus stop is at 10 o'clock met buses No. 2 and No. 9. Bus number 2 runs at an interval of 4 minutes and the bus number 9 at intervals of 9 minutes. How many times the bus meet to 18:00 local time?
• Tram stop
  The blue tram stops every 12 minutes, the red one 8 minutes. At 8 o'clock they left the stop together. How many times do they meet at a stop before 11 am?
• Trams
  Tram no. 3,7,10,11 rode together from the depot at 5am. Tram No. 3 returns after 2 hours, tram No. 7 an hour and half, no. 10 in 45 minutes and no. 11 in 30 minutes. For how many minutes and when these trams meet again?
• Tram lines
  Trams of five lines driven at intervals of 5,8,10,12 and 15 minutes. At 12 o'clock come out of the station at the same time. About how many hours again all meet? How many times have earch tram pass for this stop?
• Bus lines
  Buses connections are started from the bus stop on its regular circuit: No. 27 bus every 27 minutes and No.18 every half hour. What time started these two bus lines run if the bus stop met at 10:15 am.?
• Trams 2
  Square passes two lines of tram. One running every nine minutes, a second interval of 15 minutes. Exactly at 12 o'clock arrived two tram lines in the square. How soon should a similar situation arise again?
• Ships
  Red ship begins its circuit every 30 minutes. Blue boat begins its circuit every 45 minutes. Both ships begin their sightseeing circuit in the same place at the same time always at 10:00 o'clock. a / What time does meet boat again? b / How many times a da
• Bus lines
  At 5.00 in the morning, four buses left the terminal at the same time. The first bus has an interval of 15 minutes, the second 20 minutes, the third 25 minutes, and the fourth 45 minutes. How many minutes will all four buses leave the terminal at the same
• LCM
  What is the least common multiple of 5, 50, 14?
• Trams
  Two trams started at the same time from the same place. One tram journey takes 30 minutes and the second 45 minutes to its final stop. How long will trams meet again?
• School
  Headteacher think whether the distribution of pupils in race in groups of 4,5,6,9 or 10. How many pupils must have at least school at possible options?
• Dinosaurs
  More than 30 and less than 60 dinosaurs have met at the pond. A quarter of them bathed and 1/7 saws and the rest gripped. How many were at the pond? How many were there?
• Three
  Three buses follow the same circular route. The first driver is the slowest because he has many stops, and it takes him 90 minutes to cross the route. The second driver will pass the circuit in 1 hour. The third driver has the fewest stops, and the circui
• LCM
  Common multiple of three numbers is 3276. One number is in this number 63 times, second 7 times, third 9 times. What are the numbers?
• Drivers
  Driver Franta and driver Karel are friends. They leave the start-stop both at the same time in the afternoon - at 13.30. When will they meet again if Franta goes around his route in 50 minutes and Karel in 40 minutes?
• Three lines
  At 6 am, three bus lines are departing from the station. The first line has an interval of 24 minutes. The second line has an interval of 15 minutes. The third line runs at regular intervals of more than 1 minute. The third line runs at the same time as t
• Two buses
  The first bus runs 15 minutes the second bus runs after 21 minutes. Together they both leave at 7:00 on Monday. When and what day will they meet?