Question

Для перевозки груза предполагалось использовать равное число машин грузоподъемностью 4 т и 3 т. Но в назначенное время машин первой группы прибыло на 2 меньше, а машин второй группы – на 3 больше, чем планировалось. Первая группа машин увезла на 5 т груза меньше, чем вторая. На скольких машинах предполагалось вывезти весь груз? С объяснением пожалуйста!

Answer 1

Ответ ответ ответ ответ ответ ответ ответ Машин должно бвло быть 12+12=24 машин вместе.

Answer 2

Problem Analysis

To solve this problem, we need to determine the number of trucks required to transport the entire load. We are given that there were two groups of trucks, one with a capacity of 4 tons and the other with a capacity of 3 tons. However, the actual number of trucks in each group and the amount of cargo transported by each group differs from the planned values.

Given Information

- Number of trucks in the first group arrived 2 less than planned. - Number of trucks in the second group arrived 3 more than planned. - The first group of trucks transported 5 tons less cargo than the second group.

Solution

Let's assume the planned number of trucks in each group is x.

The actual number of trucks in the first group is x - 2, and the actual number of trucks in the second group is x + 3.

The cargo transported by the first group is 5 tons less than the cargo transported by the second group.

To find the number of trucks required to transport the entire load, we need to set up an equation based on the given information.

Let's denote the cargo transported by each truck in the first group as C1 and the cargo transported by each truck in the second group as C2.

The total cargo transported by the first group is (x - 2) * C1, and the total cargo transported by the second group is (x + 3) * C2.

According to the given information, the total cargo transported by the first group is 5 tons less than the total cargo transported by the second group. So we can set up the equation:

(x - 2) * C1 = (x + 3) * C2 - 5

Now we need to solve this equation to find the value of x, which represents the number of trucks required to transport the entire load.

Please note that we don't have enough information to determine the values of C1 and C2, so we cannot calculate the exact number of trucks required. We can only solve for x in terms of C1 and C2.

Let's solve the equation:

(x - 2) * C1 = (x + 3) * C2 - 5

Expanding the equation:

x * C1 - 2 * C1 = x * C2 + 3 * C2 - 5

Rearranging the terms:

x * C1 - x * C2 = 2 * C1 + 3 * C2 - 5

Factoring out x:

x * (C1 - C2) = 2 * C1 + 3 * C2 - 5

Dividing both sides by (C1 - C2):

x = (2 * C1 + 3 * C2 - 5) / (C1 - C2)

So, the number of trucks required to transport the entire load is given by the expression (2 * C1 + 3 * C2 - 5) / (C1 - C2).

Please note that without knowing the values of C1 and C2, we cannot calculate the exact number of trucks required. We can only provide a general formula based on the given information.

I hope this helps! Let me know if you have any further questions.