Question

Мальчик и девочка измерили расстояние 1152 м шагами. Если шаг мальчика 72 см, а шаг девочки 64 см, сколько раз их следы будут перекрываться после начала движения?​

Answer 1

Ответ: 128

Пошаговое объяснение:

фото

Answer 2

Problem Analysis

To solve this problem, we need to find the number of times the footprints of the boy and the girl will overlap after they have walked a distance of 1152 meters. We are given that the boy's step is 72 cm and the girl's step is 64 cm.

Solution

To find the number of times their footprints will overlap, we need to determine the least common multiple (LCM) of the lengths of their steps. The LCM will give us the distance at which their footprints will align again.

The LCM of two numbers can be found by dividing their product by their greatest common divisor (GCD). In this case, we need to find the LCM of 72 cm and 64 cm.

Let's calculate the LCM using the formula:

LCM(a, b) = (a * b) / GCD(a, b)

Calculation

The GCD of 72 and 64 can be found using the Euclidean algorithm or by prime factorization. In this case, we will use the Euclidean algorithm.

Step 1: Find the remainder of dividing 72 by 64: 72 % 64 = 8

Step 2: Replace 72 with 64 and 64 with the remainder from step 1: 64 % 8 = 0

Since the remainder is 0, the GCD of 72 and 64 is 8.

Now, let's calculate the LCM:

LCM(72, 64) = (72 * 64) / 8 = 576 cm

So, their footprints will align again after walking a distance of 576 cm.

To find the number of times their footprints will overlap after walking a distance of 1152 m, we need to convert 1152 m to centimeters:

1152 m = 1152 * 100 cm = 115200 cm

Now, we can divide the total distance by the LCM to find the number of times their footprints will overlap:

Number of overlaps = 115200 cm / 576 cm = 200

Therefore, the footprints of the boy and the girl will overlap 200 times after they have walked a distance of 1152 meters.

Answer

The footprints of the boy and the girl will overlap 200 times after they have walked a distance of 1152 meters.

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