Question

Две бригады,работая вместе ,могут выполнить заказ на 2 часа.Первая бригада,если она будет работать одна,потребуется на выполнение заказа на 3 часа больше чем второй.За сколько часов может выполнить заказ одна вторая бригада?)

Answer 1

 x- работа 2-х бригад за 2 часа
(t+3) - время выполнения работы Х 1-ой бригадой
t - время выполнения работы Х 2-ой бригадой
Получаем уравнение 2X/t+2X/t+3=X
После преобразований получаем
t^2-t-6=0
 получаем t=3 и t=-2
если не учитывать отрицательный ответ,то  получаем окончательный ответ - 3часа.

Answer 2

Problem Analysis

We are given that two brigades working together can complete an order in 2 hours. The first brigade, if working alone, would take 3 hours longer than the second brigade to complete the same order. We need to determine how many hours it would take for the second brigade to complete the order alone.

Solution

Let's assume that the second brigade can complete the order in x hours. According to the given information, the first brigade would take x + 3 hours to complete the order alone.

When the two brigades work together, they can complete the order in 2 hours. This means that in 1 hour, they complete 1/2 of the order.

If the first brigade takes x + 3 hours to complete the order alone, then in 1 hour, they complete 1/(x + 3) of the order.

We can set up the following equation based on the work rates:

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

To solve this equation, we can find a common denominator and then simplify:

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

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

Cross-multiplying:

2(2x + 3) = x(x + 3)

4x + 6 = x^2 + 3x

Rearranging the equation:

x^2 - x - 6 = 0

Now we can solve this quadratic equation. Factoring or using the quadratic formula, we find that x = -2 or x = 3. Since time cannot be negative, we discard the solution x = -2.

Therefore, the second brigade can complete the order alone in 3 hours.

Answer

The second brigade can complete the order alone in 3 hours.