Question

Один самосвал может перевести стройматериалы на 24 часа скорее , чем другой. Если сначала 2/3 материалов перевезёт первый самосвал , а затем оставшуюся часть второй , то понадобится на 33 часа больше , чем при одновременной работе обоих самосвалов . За сколько часов может перевести стройматериалы первый самосвал ?

Answer 1

 Пусть работа равна $1$ , производительно соответственно каждого $x;y$ 
  $\frac{2}{3x}+\frac{1}{3y}=\frac{1}{x}+\frac{1}{y}-33\\ \frac{1}{x}-\frac{1}{y}=24\\\\ \frac{2x+y}{3xy}=\frac{3x+3y-99xy}{3xy}\\\\ 99xy-2x-y=0\\ \frac{1}{x}=24+\frac{1}{y}$
решая уравнение получаем 
 $x=\frac{1}{49}\\ y=\frac{1}{25}$
 за $49$ часов

Answer 2

Problem Analysis

We are given that one dump truck can transport construction materials in less time than another dump truck. If the first dump truck transports 2/3 of the materials and then the remaining portion is transported by the second dump truck, it will take 33 hours longer than if both dump trucks were working simultaneously. We need to determine how many hours it would take for the first dump truck to transport all the construction materials.

Solution

Let's assume that the first dump truck can transport the materials in x hours. Therefore, the second dump truck can transport the same amount of materials in x + 33 hours.

According to the given information, the first dump truck transports 2/3 of the materials in x hours. This means that the remaining 1/3 of the materials will be transported by the second dump truck in x + 33 hours.

To find the total time it takes for both dump trucks to transport all the materials, we can set up the following equation:

(2/3)x + (1/3)(x + 33) = 24

Simplifying the equation:

(2/3)x + (1/3)x + 11 = 24

Combining like terms:

(5/3)x + 11 = 24

Subtracting 11 from both sides:

(5/3)x = 13

Multiplying both sides by 3/5 to isolate x:

x = (3/5) * 13

Simplifying:

x = 39/5

Therefore, it would take the first dump truck 39/5 hours to transport all the construction materials.

Answer

The first dump truck can transport all the construction materials in 7.8 hours.

Explanation

Given that the first dump truck can transport 2/3 of the materials in x hours, we can calculate the time it takes for the first dump truck to transport all the materials using the equation (2/3)x = 24. Solving for x, we find that x = 36/5 hours. Therefore, the first dump truck can transport all the construction materials in 7.8 hours.