Question

1. Папа и Денис ре­ши­ли из­ме­рить ша­га­ми рас­сто­я­ние от дома до речки. Сна­ча­ла его из­ме­рял папа, а затем с той же точки и по той же тро­пин­ке пошел Денис. На каком рас­сто­я­нии от точки стар­та их следы сов­па­ли в пер­вый раз, если шаг папы равен 90 см, а шаг Де­ни­са – 70 см?

Answer 1

90*7=70*9=630см
Ответ:630см

Answer 2

Problem Analysis

Papa and Denis measured the distance from their home to the river using their respective strides. Papa's stride is 90 cm, and Denis's stride is 70 cm. We need to find the distance from the starting point where their footprints coincided for the first time.

Solution

To find the distance from the starting point where their footprints coincided for the first time, we can use the concept of the least common multiple (LCM) of their strides.

The LCM of two numbers is the smallest number that is a multiple of both numbers. In this case, we want to find the smallest distance from the starting point where both Papa and Denis's strides will coincide.

Calculation

The LCM of 90 cm and 70 cm can be calculated as follows:

Step 1: Find the prime factorization of each number: - 90 = 2 * 3^2 * 5 - 70 = 2 * 5 * 7

Step 2: Take the highest power of all prime factors: - LCM = 2 * 3^2 * 5 * 7 = 2 * 9 * 5 * 7 = 630 cm

Therefore, the footprints of Papa and Denis will coincide for the first time at a distance of 630 cm from the starting point.