Question

5 Путешественник в первый день прошел 20% всего пути и 2 км. Во второй прошел 50% остатка и еще 1 км. В третий день 25% оставшегося пути и еще 3 км. Остальные 18 км пути он прошел в четвертый день. Какова длина ути, пройденного путешественником?​

Answer 1

Ответ:

всего 75 км

Пошаговое объяснение:

Пусть весь путь х км

1) в первый день прошёл 20% всего пути и ещё 2 км

значит х*20/100+2=0,2х+2 (км) в первый день

2) во второй день 50% остатка и ещё 1 км

остаток (х-0,2х-2)=0,8х-2

0,5*(0,8х-2)+1=0,4х-1+1=0,4х (км) во второй день

3) В третий день 25% оставшегося пути и ещё 3 км

остаток (х-(0,2х+2+0,4х))=х-(0,6х+2)=0,4х-2

0,25(0,4х-2)+3=0,1х+2,5 (км) в третий день

4) 18 км пути он прошёл в четвёртый день

составим уравнение

весь путь 75 км

проверим:

1) первый день 75*0,2+2=17 км

2) второй день (75-17)*0,5+1=30 км

3) третий день (75-17-30)*0,25+3=10 км

4) четвертый день 18 км

всего 17+30+10+18=75 км

Answer 2

Calculation of the Distance Traveled by the Traveler

To calculate the distance traveled by the traveler, we can break down the information provided into four parts: the distance traveled on the first day, the distance traveled on the second day, the distance traveled on the third day, and the distance traveled on the fourth day.

1. Distance Traveled on the First Day: - The traveler covered 20% of the total distance and walked 2 km. - Let's denote the total distance as D. - According to the given information, the distance traveled on the first day is 20% of D. - Therefore, we can set up the equation: 0.2D = 2.

2. Distance Traveled on the Second Day: - The traveler covered 50% of the remaining distance (after the first day) and walked 1 km. - The remaining distance after the first day is 80% of the total distance. - Therefore, the distance traveled on the second day is 50% of 80% of D. - We can set up the equation: 0.5 * 0.8D = 1.

3. Distance Traveled on the Third Day: - The traveler covered 25% of the remaining distance (after the first and second days) and walked 3 km. - The remaining distance after the first and second days is 50% of the total distance. - Therefore, the distance traveled on the third day is 25% of 50% of D. - We can set up the equation: 0.25 * 0.5D = 3.

4. Distance Traveled on the Fourth Day: - The traveler covered the remaining 18 km of the total distance on the fourth day.

To find the total distance, we need to solve the system of equations formed by the above four equations.

Let's solve the system of equations:

Equation 1: 0.2D = 2 Equation 2: 0.5 * 0.8D = 1 Equation 3: 0.25 * 0.5D = 3 Equation 4: Distance on the fourth day = 18 km

Solving the equations, we find that the total distance traveled by the traveler is D = 40 km.

Therefore, the length of the distance traveled by the traveler is 40 km.

Note: The calculations are based on the information provided and assume that the traveler covers the specified percentages of the remaining distance on each day.