Question

Саша и Миша одновременно начали двигаться в одном направлении. Длина шага Саши- 65 см Длина шага Мишы- 75 см Ск. раз их шаги совпадали, если они прошли всего 195 метров? прошу, срочно решите задачку.

Answer 1

250 или 300 киллометро

Answer 2

Problem Analysis

We are given that Sasha and Misha are moving in the same direction simultaneously. Sasha's stride length is 65 cm, and Misha's stride length is 75 cm. We need to determine how many times their strides coincide if they have covered a total distance of 195 meters.

Solution

To solve this problem, we can use the concept of the least common multiple (LCM) of two numbers. The LCM of two numbers is the smallest multiple that is divisible by both numbers. In this case, we need to find the LCM of Sasha's stride length (65 cm) and Misha's stride length (75 cm).

The LCM can be calculated using the formula: LCM(a, b) = (a * b) / GCD(a, b)

Here, GCD(a, b) represents the greatest common divisor of a and b.

Let's calculate the LCM of 65 cm and 75 cm:

LCM(65, 75) = (65 * 75) / GCD(65, 75)

To find the GCD of 65 and 75, we can use the Euclidean algorithm. The Euclidean algorithm states that the GCD of two numbers can be found by repeatedly subtracting the smaller number from the larger number until the two numbers become equal.

Let's calculate the GCD of 65 and 75:

GCD(65, 75) = GCD(75 - 65, 65) = GCD(10, 65) = GCD(65, 10) = GCD(10, 5) = GCD(5, 10) = GCD(10 - 5, 5) = GCD(5, 5) = 5

Now, we can substitute the values into the LCM formula:

LCM(65, 75) = (65 * 75) / GCD(65, 75) = (65 * 75) / 5 = 13 * 75 = 975 cm

So, Sasha and Misha's strides will coincide every 975 cm.

To find the number of times their strides coincide in a distance of 195 meters (19500 cm), we can divide the total distance by the length of each stride:

Number of coinciding strides = Total distance / LCM(65, 75) = 19500 / 975 = 20

Therefore, Sasha and Misha's strides will coincide 20 times if they have covered a total distance of 195 meters.

Answer

Sasha and Misha's strides will coincide 20 times if they have covered a total distance of 195 meters.