Question

.

A water tank fills through two pipes. Water flows in
through one pipe at a rate of 25,000 gallons per hour
and in through the other pipe at a rate of 45,000
gallons per hour. Water leaves the system at a rate of
60,000 gallons per hour.
There are 3 of these tanks, and each tank holds
1 million gallons. Each tank is half full. Water is
entering and leaving a tank at the maximum
amounts. Determine the number of hours, x, it will
take to fill all 3 tanks one at a time.​

Answer 1

To fill all 3 tanks one at a time, it will take 10 hours.

Step-by-step explanation:

To determine the number of hours it will take to fill all 3 tanks one at a time, we need to calculate the net rate at which water is being filled in the tanks.

Each tank is being filled from two pipes, one at a rate of 25,000 gallons per hour and the other at a rate of 45,000 gallons per hour. Since there are 3 tanks, the total incoming rate would be 3 times the sum of the individual rates, which is 3 x (25,000 + 45,000) = 3 x 70,000 = 210,000 gallons per hour.

Water leaves the system at a rate of 60,000 gallons per hour. Therefore, the net rate at which water is being filled in the tanks is 210,000 - 60,000 = 150,000 gallons per hour.

Each tank can hold 1 million gallons and is currently half full, which means it needs to be filled with 500,000 gallons.

So, the number of hours it will take to fill all 3 tanks one at a time can be calculated by dividing the required total amount of water (3 x 500,000 = 1,500,000 gallons) by the net rate at which water is being filled in the tanks (150,000 gallons per hour).

Number of hours = 1,500,000 / 150,000 = 10 hours

Answer 2

It will take 150 hours to fill all 3 tanks at a time.

Step-by-step explanation:

Water flows in pipe 1 at a rate of 25,000 gallons per hour.

Other pipe at a rate of 45,000 gallons per hour.

Water leaves the system at a rate of 60,000 gallons per hour.

There are 3 of these tanks and each tank holds 1 million gallons.

Each tank is half full.

So, total capacity of 3 tanks = 3 millions and it is half full.

The water need to be filled = 1.5 millions. At the same time 60,000 gallons of water leaving out.

25,000 x + 45,000 x - 60,000 x = 1.5 millions

70,000x -60,000x = 1500000

10,000x = 1500000

Dividing both sides by 10,000, we get

x = 150 hours

Therefore, it will take 150 hours to fill all 3 tanks at a time.