Question

Лыжники маршрут протяженностью в 105 км прошли за три дня. Во второй день прошли 3/4 расстояния, оставшегося после первого дня пути, а в третий день на 5 км меньше, чем в первый день. Найти протяженность пути за каждый день.

Answer 1

Первый день - х (км)

Второй день - (105 - х) * 3/4 (км)

Третий день - (х - 5) км

Протяжённость всего маршрута 105 км, дробь 3/4 = 0,75 (в десятичных)

х + 0,75 * (105 - х) + (х - 5) = 105

х + 78,75 - 0,75х + х - 5 = 105

1,25х = 105 - 78,75 + 5

1,25х = 31,25

х = 31,25 : 1,25 = 25 (км) - прошли в первый день

0,75 * (105 - 25) = 0,75 * 80 = 60 (км) - прошли во второй день

25 - 5 = 20 (км) - прошли в третий день

Весь маршрут: 25 + 60 + 20 = 105 (км) 

Answer 2

Calculating the Distance Covered Each Day by Skiers

To calculate the distance covered each day by the skiers, we can use the information provided in the question. Let's break it down step by step.

1. Total Distance and Time Taken: - The skiers covered a route with a total distance of 105 km over three days.

2. Distance Covered on the Second Day: - On the second day, the skiers covered 3/4 of the remaining distance after the first day.

3. Distance Covered on the Third Day: - On the third day, the skiers covered 5 km less than they did on the first day.

Calculation

1. Total Distance Covered: - Total distance covered = 105 km.

2. Distance Covered on the First Day: - Let's assume the distance covered on the first day is x km. - Distance covered on the second day = 3/4 * (105 - x) km.

3. Distance Covered on the Third Day: - Distance covered on the third day = x - 5 km.

Solving for x

We can set up an equation to solve for the distance covered on the first day (x).

- x + 3/4 * (105 - x) + (x - 5) = 105 - 4x + 3(105 - x) + 4(x - 5) = 420 - 4x + 315 - 3x + 4x - 20 = 420 - 5x + 295 = 420 - 5x = 420 - 295 - 5x = 125 - x = 125 / 5 - x = 25

Results

- Distance Covered on the First Day: 25 km - Distance Covered on the Second Day: 3/4 * (105 - 25) = 60 km - Distance Covered on the Third Day: 25 - 5 = 20 km