# 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 the first, also at the same time as the second, and sometimes runs alone. Find the interval of the 3rd line.

Result

t3 =  3 min

#### Solution:

$t_{ 1 } = 24 \ min \ \\ t_{ 2 } = 15 \ min \ \\ \ \\ t_{ 3 }>1 \ \\ \ \\ SD(t_{ 1 },t_{ 2 }): 1, 3 \ \\ \ \\ 24 = 2^3 \cdot 3 \\ 15 = 3 \cdot 5 \\ \text{GCD}(24, 15) = 3 = 3\\ \ \\ \ \\ t_{ 3 } = GCD(t_{ 1 },t_{ 2 }) = GCD(24,15) = 3 = 3 \ \text { min }$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...): Be the first to comment! #### Following knowledge from mathematics are needed to solve this word math problem:

Do you want to calculate greatest common divisor two or more numbers?

## Next similar math problems:

1. Lcm of three numbers What is the Lcm of 120 15 and 5
2. Two-digit number I am a two-digit number less than 20. When I divided by three, then you get the rest 1 and when you divide me by four you get also rest 1. What number am I? The children of the tennis school received 64 white and 48 yellow balls from the sponsor. When asked about how many balls they could take, they were answered: "You have so many that none of you will have more than 10 balls and all will have the same number
4. Quotient Find quotient before the bracket - the largest divisor 51 a + 34 b + 68 121y-99z-33
5. Turtles Žofka and Julka Gray wolf kept in his tent turtles Žofka and Julka, which together have 200 years. After 50 years will Julka 2 times older than Žofka. How old are the turtles?
6. Write decimals Write in the decimal system the short and advanced form of these numbers: a) four thousand seventy-nine b) five hundred and one thousand six hundred and ten c) nine million twenty-six
7. Digits of age The product of the digits of Andrew age as 6 years ago and not equal to 0. Andrew age is also the smallest possible age with this two conditions. After how many years will be the product of the digits of Andrew age again the same as today?
8. Common divisors Find all common divisors of numbers 30 and 45.
9. Number What number should be placed instead of the asterisk in number 702*8 to get a number divisible by 6?
10. Counting number What is the smallest counting number divisible by 2,5,7,8 and 15?
11. Suzan Susan's age will be after 12 years four times as much as twelve years ago. How old is Susan now?
12. To improve To improve her handwriting Paula practices writing the numbers 1 to 200 in words. How many times will she have written the word "one" in all?
13. 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?
14. Prime factors Write 98 as product of prime factors
15. Last page Two consecutive sheets dropped out of the book. The sum of the numbers on the sides of the dropped sheets is 154. What is the number of the last page of the dropped sheets?
16. Family 8 Father is 38 years old, daughter 12, son 14. How many years will father have as many years as his children together?
17. Bicycle wheels Driving wheel of a bicycle has 54 teeth. The driven wheel has 22 teeth. After how many revolutions will meet the same teeth?