Question

Саша тренировал глазомер, оценивая длину некоторой дистанции вдоль шоссе. При первой попытке он оценил её в 120 шагов. Оказалось, что за 120 шагов он не дошёл до конца дистанции на 0,2 её длины. В какое количество шагов он оценил длину дистанции при второй попытке, если за это количество шагов он удалился от её конца на 0,1 её длины и Сашины шаги были одинаковыми при обеих попытках? А. В 130 шагов. Б. В 140 шагов. В. В 150 шагов. Г. В 165 шагов.

Answer 1

Пусть длина дистанции равна х. Тогда Саша не дошёл в первый раз до конца х/5 шагов. Значит он прошёл х-(х/5)=(4/5)x
(4/5)x=120
x=150
во второй попытке он прошёл дальше конца на х/10. То есть всего он прошёл во второй раз (11/10)x
подставляем значение х=150
(11/10)x=(11·150)/10=165
ответ Г

Answer 2

Problem Analysis

Sasha estimated the length of a distance along a highway by counting the number of steps it took him to reach the end. In his first attempt, he estimated the distance to be 120 steps but found that he fell short of the end by 0.2 times the length of the distance. In his second attempt, he estimated the distance to be a certain number of steps and found that he fell short of the end by 0.1 times the length of the distance. We need to determine the number of steps Sasha estimated in his second attempt.

Solution

Let's assume the length of the distance is represented by 'x' and the number of steps Sasha estimated in his second attempt is represented by 'n'.

In Sasha's first attempt, he estimated the distance to be 120 steps but fell short of the end by 0.2 times the length of the distance. This can be represented as the equation:

120 = x - 0.2x

Simplifying the equation, we get:

0.8x = 120

x = 120 / 0.8

x = 150

Therefore, the length of the distance is 150.

In Sasha's second attempt, he estimated the distance to be 'n' steps but fell short of the end by 0.1 times the length of the distance. This can be represented as the equation:

n = x - 0.1x

Substituting the value of x, we get:

n = 150 - 0.1 * 150

Simplifying the equation, we get:

n = 150 - 15

n = 135

Therefore, Sasha estimated the length of the distance to be 135 steps in his second attempt.

Answer

Sasha estimated the length of the distance to be 135 steps in his second attempt.