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Question

# A 10,000 gallon swimming pool needs to be emptied. Exactly 2000 gallons have already been pumped out of the pool and into the tanker. How can you determine how long it will take to pump all of the water into the tanker. 720 gallons per hour can be emptied from the pool.

Hint:

### We are given the rate at which water can be emptied from the pool. We are given the initial value of how much water has already been pumped. This information helps us to find a relationship between the quantity of water in the pool and the time taken to pump the water out of the pool. We construct a linear function and we find the time taken to pump out the water from the equation

## The correct answer is: 11.11

*Step by step solution*:

Let the time (in hours) taken be denoted by x and let the quantity of water in the pool be denoted by y.

First, we find a linear function representing the relationship between x and y

Given,

The rate at which the water is pumped= 720 gallons per hour

Quantity of water already pumped out = 2000 gallons

The total quantity of water in the pool = 10000 gallons

From the slope intercept form of an equation y = mx + c, where m is slope and c is the y-intercept,

And using the values m=720 and c =2000, we get

We need to pump out 10000 gallons of water, so putting y= 10000 in the above equation, we get

10000 = 720x + 2000

Next, we solve for x,

Dividing by 720 throughout, we have

Thus, we will need 11.11 hours to empty the pool.

We need to pump out 10000 gallons of water, so putting y= 10000 in the above equation, we get

Next, we solve for x,

Dividing by 720 throughout, we have

Thus, we will need 11.11 hours to empty the pool.

We can also solve this problem without the use of functions. There is 10000 gallons of water and 2000 gallons of water is already emptied. So there is (10000-2000=) 8000 gallons of water. It is given that the rate at which water is pumped is 720 gallons per hour. So the time taken is hours

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