Question

Решите задачу рациональным способом чтобы добраться до места назначения Путешественники ехали три дня В первый день они проехали 30% всего пути без 20 километра во второй день они проехали 60% оставшегося пути без 10 километров и на третий день ему стало проехать 130 километров

Answer 1

Пусть х, км - расстояние от начального пункта до пункта назначения, тогда 0,3х-20, км прошли путешественники в 1-й день, (х-(0,3х-20))*0,6-10, км прошли путешественники во 2-й день. От всего расстояния отнимем расстояние, которое прошли путешественники за 2 дня и останется 130 км. - то, что осталось пройти. Составим уравнение:
х-(0,3х-20)-((х-(0,3х-20))*0,6-10)=130
х-0,3х+20-(х-0,3х+20)*0,6+10=130
х-0,3х+20-0,6х+0,18х-12+10=130
0,28х=130-20+12-10
0,28х=112
х=112:0,28=400 км - расстояние от начального пункта до пункта назначения
0,3*400-20=120-20=100 км прошли путешественники в первый день
Ответ: 1) на расстоянии 400 км от начального пункта находится пункт назначения путешественников;
2) 100 км прошли путешественники в первый день.

Answer 2

Problem Analysis

To solve this problem, we need to determine the total distance traveled by the travelers and the distance traveled each day. We are given that on the first day, they traveled 30% of the total distance minus 20 kilometers, on the second day they traveled 60% of the remaining distance minus 10 kilometers, and on the third day, they traveled 130 kilometers.

Solution

Let's denote the total distance as D and the distance traveled on each day as D1, D2, and D3 respectively. We can set up the following equations:

1. On the first day, they traveled 30% of the total distance minus 20 kilometers: D1 = 0.3D - 20.

2. On the second day, they traveled 60% of the remaining distance minus 10 kilometers: D2 = 0.6(D - D1) - 10.

3. On the third day, they traveled 130 kilometers: D3 = 130.

To find the total distance D, we can substitute the values of D1 and D2 from equations 1 and 2 into equation 3 and solve for D.

Let's solve the equations step by step:

1. Substitute the value of D1 from equation 1 into equation 2: D2 = 0.6(D - (0.3D - 20)) - 10.

2. Simplify equation 2: D2 = 0.6(D - 0.3D + 20) - 10.

3. Combine like terms: D2 = 0.6(0.7D + 20) - 10.

4. Distribute 0.6 to the terms inside the parentheses: D2 = 0.42D + 12 - 10.

5. Simplify: D2 = 0.42D + 2.

6. Substitute the value of D2 from equation 5 into equation 3: 130 = 0.42D + 2.

7. Solve for D: 0.42D = 130 - 2, 0.42D = 128, D = 128 / 0.42.

8. Calculate the value of D: D ≈ 304.76.

Now that we have found the total distance D, we can substitute this value back into equations 1 and 2 to find the distances traveled on the first and second days.

9. Substitute the value of D into equation 1: D1 = 0.3(304.76) - 20.

10. Calculate the value of D1: D1 ≈ 62.43.

11. Substitute the value of D into equation 2: D2 = 0.6(304.76 - 62.43) - 10.

12. Calculate the value of D2: D2 ≈ 133.94.

Therefore, the total distance traveled is approximately 304.76 kilometers, the distance traveled on the first day is approximately 62.43 kilometers, and the distance traveled on the second day is approximately 133.94 kilometers.

Answer

The total distance traveled by the travelers is approximately 304.76 kilometers. On the first day, they traveled approximately 62.43 kilometers, and on the second day, they traveled approximately 133.94 kilometers.

Please note that the values provided are approximate due to rounding.

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