Question

Туристы прошли маршрут за три дня. В первый день они прошли 1/7 часть маршрута и ещё 4 км. Во второй день прошли 25% оставшегося пути и ещё 6 км. В третий день прошли 5/9 оставшегося пути и последние 8 км. Сколько км содержал весь маршрут? Ответ 42 км.

Answer 1

Нехай х весь маршрут
1/7х+4 км за 1 день
в 2 день- 1/4(1/7+4)+6 км
в 3 день- 5/9(1/4(1/7+4)+6)+8
5/9(1/4(1/7+4)+6)+8=42

Answer 2

Problem Analysis

The problem states that a group of tourists completed a route in three days. On the first day, they covered 1/7 of the route plus an additional 4 km. On the second day, they covered 25% of the remaining distance plus another 6 km. On the third day, they covered 5/9 of the remaining distance plus the final 8 km. We need to determine the total distance of the entire route.

Solution

To find the total distance of the entire route, we need to calculate the distance covered on each day and add them together.

Let's break down the problem step by step:

1. On the first day, the tourists covered 1/7 of the route plus an additional 4 km. 2. On the second day, they covered 25% of the remaining distance plus another 6 km. 3. On the third day, they covered 5/9 of the remaining distance plus the final 8 km.

To calculate the total distance, we'll add up the distances covered on each day.

Calculation

1. Distance covered on the first day: - 1/7 of the route + 4 km

2. Distance covered on the second day: - 25% of the remaining distance + 6 km

3. Distance covered on the third day: - 5/9 of the remaining distance + 8 km

To find the remaining distance on the second day, we need to subtract the distance covered on the first day from the total distance.

Let's denote the total distance as D.

1. Remaining distance on the second day: - D - (1/7 * D + 4 km)

To find the remaining distance on the third day, we need to subtract the distance covered on the second day from the remaining distance on the second day.

2. Remaining distance on the third day: - (D - (1/7 * D + 4 km)) - (25% * (D - (1/7 * D + 4 km)) + 6 km)

Finally, we can calculate the total distance by adding up the distances covered on each day:

Total distance = Distance covered on the first day + Distance covered on the second day + Distance covered on the third day

Let's calculate the total distance step by step.

Calculation Steps

1. Remaining distance on the second day: - D - (1/7 * D + 4 km)

2. Remaining distance on the third day: - (D - (1/7 * D + 4 km)) - (25% * (D - (1/7 * D + 4 km)) + 6 km)

3. Total distance: - (1/7 * D + 4 km) + (25% * (D - (1/7 * D + 4 km)) + 6 km) + (5/9 * ((D - (1/7 * D + 4 km)) - (25% * (D - (1/7 * D + 4 km)) + 6 km)) + 8 km)

Now, let's solve the equation to find the value of D, which represents the total distance of the entire route.

Calculation

1. Remaining distance on the second day: - D - (1/7 * D + 4 km) - Simplifying the equation: - D - 1/7 * D - 4 km - 6/7 * D - 4 km

2. Remaining distance on the third day: - (D - (1/7 * D + 4 km)) - (25% * (D - (1/7 * D + 4 km)) + 6 km) - Simplifying the equation: - (6/7 * D - 4 km) - (25% * (6/7 * D - 4 km) + 6 km) - (6/7 * D - 4 km