Question

Из одного места в одном направлении одновременно стартовали по велотреку два велосипедисти. один из них делает круг повелотреку за 1мин, а второй - за 45с. через какое наименьшее количество минут после начала движения велосипедисты снова встретятся в месте старта? сколько кругов по велотреку при цьму проедет Кожин из них?Длина шага Чебурашки равна 15см , а крокодила Гены- 50 см . Какое наименьшее одинаковое расстояние должен пройти каждый из них , чтобы они оба сделали по целаму числу шагов?

Answer 1

1) 4 мин 4 круга
2) 150см

Answer 2

Problem Analysis

We have two cyclists starting simultaneously in the same direction on a velodrome track. One cyclist completes a lap in 1 minute, while the other completes a lap in 45 seconds. We need to determine the minimum number of minutes it will take for the cyclists to meet again at the starting point. We also need to find out how many laps each cyclist will have completed by that time. Additionally, we are given the stride lengths of two characters, Cheburashka and Gena the Crocodile, and we need to find the minimum distance they need to travel to take an equal number of steps.

Meeting Time for the Cyclists

To find the minimum time it takes for the cyclists to meet again at the starting point, we need to find the least common multiple (LCM) of their lap times. The LCM will give us the time it takes for both cyclists to complete an integer number of laps.

The first cyclist completes a lap in 1 minute, which is equivalent to 60 seconds. The second cyclist completes a lap in 45 seconds. To find the LCM of these two lap times, we can find the LCM of 60 and 45.

Using the prime factorization method, we can find the LCM by multiplying the highest powers of all prime factors present in the numbers:

60 = 2^2 * 3 * 5 45 = 3^2 * 5

The LCM is then calculated as:

LCM = 2^2 * 3^2 * 5 = 180

Therefore, the cyclists will meet again at the starting point after 180 seconds, which is equivalent to 3 minutes.

Number of Laps Completed

To find the number of laps each cyclist will have completed by the time they meet again, we can divide the total meeting time by the lap time of each cyclist.

The first cyclist completes a lap in 1 minute, so in 3 minutes, they will have completed 3 laps.

The second cyclist completes a lap in 45 seconds, so in 3 minutes, they will have completed 4 laps.

Therefore, the first cyclist will have completed 3 laps and the second cyclist will have completed 4 laps by the time they meet again.

Minimum Distance for Equal Steps

To find the minimum distance that Cheburashka and Gena need to travel to take an equal number of steps, we need to find the least common multiple (LCM) of their stride lengths.

Cheburashka's stride length is 15 cm, and Gena's stride length is 50 cm. To find the LCM of these two stride lengths, we can find the LCM of 15 and 50.

Using the prime factorization method, we can find the LCM by multiplying the highest powers of all prime factors present in the numbers:

15 = 3 * 5 50 = 2 * 5^2

The LCM is then calculated as:

LCM = 2 * 3 * 5^2 = 150

Therefore, Cheburashka and Gena need to travel a minimum distance of 150 cm each to take an equal number of steps.

Summary

- The minimum time it will take for the cyclists to meet again at the starting point is 3 minutes. - The first cyclist will have completed 3 laps and the second cyclist will have completed 4 laps by the time they meet again. - Cheburashka and Gena need to travel a minimum distance of 150 cm each to take an equal number of steps.

Please let me know if anything is unclear or if you need further assistance!