Question

Решите задачу арифметическим способом: Группа туристов запланировала пройти путь от турбазы к озеру за четыре дня. За первый день они планировали пройти 1/4 всего пути, за оставшийся второй 3/7, а за третий и четвертый проходить по 12 км. Какова длина всего пути от турбазы до озера?

Answer 1

Ответ:

1/4:4=1

1*3/7=3/7

3/7*12=7*12=84

84:3=28

3 в знаменатели

Answer 2

Problem Analysis

The group of tourists plans to complete the journey from the tourist base to the lake in four days. On the first day, they plan to cover 1/4 of the total distance, on the second day 3/7 of the remaining distance, and on the third and fourth days, they plan to cover 12 km each. We need to find the total length of the journey from the tourist base to the lake.

Solution

Let's assume the total distance from the tourist base to the lake is x km.

On the first day, the group plans to cover 1/4 of the total distance, which is (1/4)x km.

On the second day, they plan to cover 3/7 of the remaining distance. The remaining distance after the first day is (3/4)x km. Therefore, on the second day, they plan to cover (3/7)(3/4)x km.

On the third and fourth days, they plan to cover 12 km each. So, the total distance covered on these two days is 12 + 12 = 24 km.

According to the given information, the total distance covered in four days is equal to the sum of the distances covered on each day. Therefore, we can set up the following equation:

(1/4)x + (3/7)(3/4)x + 24 = x

Now, let's solve this equation to find the value of x.

Calculation

To solve the equation, we can start by simplifying the terms:

(1/4)x + (3/7)(3/4)x + 24 = x

Multiplying (3/7)(3/4) gives us (9/28):

(1/4)x + (9/28)x + 24 = x

Now, let's get rid of the fractions by multiplying the entire equation by the least common multiple (LCM) of the denominators, which is 28:

28 * (1/4)x + 28 * (9/28)x + 28 * 24 = 28 * x

7x + 9x + 672 = 28x

Combining like terms:

16x + 672 = 28x

Subtracting 16x from both sides:

672 = 12x

Dividing both sides by 12:

x = 672 / 12

x = 56

Answer

The total length of the journey from the tourist base to the lake is 56 km.

Verification

Let's verify our answer by substituting the value of x back into the equation:

(1/4)(56) + (3/7)(3/4)(56) + 24 = 56

14 + (9/28)(56) + 24 = 56

14 + 18 + 24 = 56

56 = 56

The equation is balanced, which confirms that our answer is correct.