Question

Для откачивания воды из затопленного помещения были задействованы три насоса. Первый из них может выкачать всю воду за 12 ч, второй - за 15 ч, а третий - за 20 ч. Сначала в течение 3 ч работали первый и второй насосы, а затем подключили третий насос. За какое время была откачана вся вода

Answer 1

1 - вся вода
1/12 - откачивает за час первый
1/15 - второй
1/20 - третий
1/12+1/15=5/60+4/60=9/60=3/20 откачивают в час 1-й и 2-й
3/20*3=9/20 откачали за 3 ч 1-й и 2-й
 1-9/20=11/20 осталось откачать
 3/20+1/20=4/20=1/5 откачивают в час все три
 11/20:1/5=11/4=2 3/4 (ч) откачивали остальное все три
3 ч+2 3/4 ч=5 3/4 ч (5 ч 45 мин)
Ответ: вся вода была откачана за 5 3/4 ч (5 ч 45 мин)

Answer 2

Calculating Time to Pump Out Water

To calculate the time it took to pump out all the water from the flooded area, we can follow these steps:

1. Calculate the Combined Pumping Rate: First, we need to calculate the combined pumping rate of the first two pumps working together for 3 hours. 2. Calculate the Remaining Water: Then, we'll calculate the remaining water after the first two pumps worked for 3 hours. 3. Calculate the Time Taken by the Third Pump: Finally, we'll determine how long it took for the third pump to pump out the remaining water.

Step 1: Calculate the Combined Pumping Rate

The combined pumping rate of the first two pumps working together for 3 hours can be calculated using the formula: \[ \text{Combined Pumping Rate} = \frac{1}{\frac{1}{\text{First Pump Rate}} + \frac{1}{\text{Second Pump Rate}}} \]

Using this formula, we can calculate the combined pumping rate.

Step 2: Calculate the Remaining Water

After the first two pumps worked for 3 hours, we need to calculate the remaining water that the third pump needs to pump out. This can be calculated using the formula: \[ \text{Remaining Water} = \text{Total Water} - \text{Water Pumped by First Two Pumps in 3 Hours} \]

Step 3: Calculate the Time Taken by the Third Pump

Finally, we can calculate the time it took for the third pump to pump out the remaining water using the formula: \[ \text{Time Taken by Third Pump} = \frac{\text{Remaining Water}}{\text{Third Pump Rate}} \]

Let's proceed with the calculations.

Calculations

1. Calculate the Combined Pumping Rate: - Using the given pumping rates, the combined pumping rate is: \[ \text{Combined Pumping Rate} = \frac{1}{\frac{1}{12} + \frac{1}{15}} = \frac{1}{\frac{5}{60} + \frac{4}{60}} = \frac{1}{\frac{9}{60}} = \frac{60}{9} = 6.67 \]

2. Calculate the Remaining Water: - Assuming the total amount of water is 1 unit, the water pumped out by the first two pumps in 3 hours is: \[ \text{Water Pumped by First Two Pumps in 3 Hours} = 3 \times \text{Combined Pumping Rate} = 3 \times 6.67 = 20 \]

- Therefore, the remaining water is: \[ \text{Remaining Water} = 1 - 20 = 0.8 \]

3. Calculate the Time Taken by the Third Pump: - The time taken by the third pump to pump out the remaining water is: \[ \text{Time Taken by Third Pump} = \frac{0.8}{\frac{1}{20}} = 16 \]

Conclusion

The third pump took 16 hours to pump out the remaining water after the first two pumps worked for 3 hours.

Therefore, the total time taken to pump out all the water was 19 hours (3 hours for the first two pumps + 16 hours for the third pump).