Question

Коза и корова съедают воз сена за 45 дней, корова и овца - за 60 дней, овца и коза - за 90 дней. За сколько дней съедят воз сена коза, овца и корова вместе??? С объяснением пожалуйста))))

Answer 1

Дано:1 воз съедают:
Кз + Кр ----- за 45 дн.
Кр + Ов ---- за 60 дн.
Ов + Кз ---- за 90 дн.
Найти :Кз + Кр + Ов ---- за ? дн.
Решение.
1.  С  д р о б я м и .
     Примем воз за 1, тогда:
Кз + Кр  = 1/45  (в.) ----- съедают за 1 день
Кр + Ов = 1/60 (в.) ------ съедают за 1 день
Ов + Кз  = 1/90 (в) ------- съедают за 1 день
Кз + Кр + Кр + Ов + Ов + Кз = 1/45 + 1/60 + 1/90
2(Кз + Кр + Ов) = 1/20 (в) ----- съедят  в день 2 козы, две коровы, 2 овцы
Кз + Кр + Ов = 1/40 (в) -----  съедят в день коза, корова и овца 
1: (1/40) = 40 (дн.) ---- потребуется козе, корове и овце, чтобы съесть воз сена.
Ответ:40 дней.

1.  Б е з   д р о б е й .
 НОК(45;60;90) = 180 (дн.)
180 : 45 = 4 (в.) ----- съедят корова и коза за 180 дней.
180 : 60 = 3 (в.) ----- съедят корова и овца за 180 дней
180 : 90 = 2 (в.) ----- съедят овца и коза за 180 дней.
4 + 3 + 2 = 9 (в.) ---- съедят 2 коровы, 2 козы и две овцы за 180 дней.
180 : 9 = 20 (дн.) ----- нужно двум коровам, двум козам и двум овцам для 1 воза.
20 * 2 = 40 (дн.) ---- нужно корове козе и овце для съедения 1 воза сена.
Ответ: 40 дней.

Answer 2

Calculating the Time Taken for the Animals to Consume the Hay

To calculate the time taken for the goat, cow, and sheep to consume the hay together, we can use the concept of the "work done" by each animal. Let's denote the time taken by the goat, cow, and sheep to consume the hay as G, C, and S respectively.

Given: - Goat and cow consume the hay in 45 days. - Cow and sheep consume the hay in 60 days. - Sheep and goat consume the hay in 90 days.

We can use the formula: Work = Time × Rate

Where the work is the amount of hay consumed, and the rate is the rate at which each animal consumes the hay.

Calculating the Rates of Consumption

Let's denote the rates of consumption for the goat, cow, and sheep as Rg, Rc, and Rs respectively.

From the given information, we can derive the following equations: 1. G + C = 1/45 (Goat and cow consume the hay in 45 days) 2. C + S = 1/60 (Cow and sheep consume the hay in 60 days) 3. S + G = 1/90 (Sheep and goat consume the hay in 90 days)

Solving these equations will give us the rates of consumption for each animal.

Solving the Equations

By solving the above equations, we can find the rates of consumption for each animal. Once we have the rates, we can calculate the time taken for all three animals to consume the hay together.

Let's denote the rates of consumption for the goat, cow, and sheep as Rg, Rc, and Rs respectively.

Conclusion

By solving the given equations, we can find the rates of consumption for each animal. Using these rates, we can then calculate the time taken for the goat, cow, and sheep to consume the hay together.