Question

1) В одном цистерне в 4 раза меньше нефти чем во втором. После того как в первую цистерну добавили 20 т нефти, а из второй откачали 19 т нефти в обеих цистернах стало поровну. Сколько тон нефти было в каждой цистерне первоначально 2)Туристы были в пути 3 дня. В первый день они преодолели 36% всего расстояния, во второй -52% оставшегося, а в третий -54 км. Найдите длину всего пути

Answer 1

1) Предположим что в 1 цистерне - х т нефти, а во второй 4х
х + 20 = 4х - 19
20 + 19 = 4х - х
39 = 3х
х = 13
1 цистерна - 13 т нефти
2 цистерна - 4 * 13 = 52 т нефти
Ответ: 13 т, 52 т.

Answer 2

Task 1: Calculating Initial Oil Quantities in the Tanks

To solve this problem, we can use a system of linear equations. Let's denote the initial quantities of oil in the first and second tanks as x and y, respectively.

According to the given information: 1. In the first tank, after adding 20 tons of oil, the quantity becomes x + 20. 2. In the second tank, after removing 19 tons of oil, the quantity becomes y - 19. 3. Both tanks have the same quantity of oil after these operations, so we have the equation: x + 20 = y - 19.

We also know that the quantity of oil in the first tank is 4 times less than in the second tank, so we have the equation: x = (1/4)y.

We can solve these two equations to find the initial quantities of oil in each tank.

Let's proceed with the calculations.

Calculations:

Using the given equations: 1. x + 20 = y - 19 2. x = (1/4)y

We can solve for x and y.

Substituting the value of x from equation 2 into equation 1: (1/4)y + 20 = y - 19 20 + 19 = y - (1/4)y 39 = (3/4)y y = 39 * (4/3) y = 52

Substituting the value of y back into equation 2: x = (1/4)*52 x = 13

Answer:

The initial quantity of oil in the first tank was 13 tons, and in the second tank was 52 tons.

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Task 2: Finding the Total Distance of the Tourists' Journey

To find the total distance of the tourists' journey, we can use the information provided about the percentages of the distance covered on each day.

Let's denote the total distance of the journey as D. According to the given information: 1. On the first day, they covered 36% of the total distance. 2. On the second day, they covered 52% of the remaining distance. 3. On the third day, they covered the remaining 54 km.

We can use this information to calculate the total distance of the journey.

Calculations:

Let's denote the total distance as D.

According to the given information: 1. Distance covered on the first day = 0.36D 2. Remaining distance after the first day = D - 0.36D = 0.64D 3. Distance covered on the second day = 0.52 * 0.64D = 0.3328D 4. Remaining distance after the second day = 0.64D - 0.3328D = 0.3072D 5. Distance covered on the third day = 54 km

We can set up the equation: 0.3072D = 54

Solving for D: D = 54 / 0.3072

Answer:

The total distance of the tourists' journey was approximately 175.78 km.