Question

Bruno works for Poseidon Pool Service. He needs to drain a 38,000-gallon pool so that he can repair the cracked plaster. The Pool drains 12 gallons per minute.

Write an equation to represent the pool draining in slope-intercept form.


How long will it take for the pool to fully drain? Explain using numbers and words


Bruno needs to refill the pool now that the plaster is repaired. The Pool fills 16 gallons per minute.


Write an equation in slope intercept form to represent the pool filling back up.

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How long will it take for the pool to fill back up? Explain using words and numbers..

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Answer 1

We need to find the function in slope-intercept form. We thus need the y-intercept and slope. We know there are 38000 gallons in the pool already, so the y-intercept is 38000. The pool drains 12 per minute, so the slope is -12.

y = mx + b
y = -12x + 38000

To find the time it takes to drain the pool, we need to find x where y = 0, so we set the equation to 0 and solve for x.

0 = -12x + 38000
-38000 = -12x
-38000/-12 = -12x/-12
3167 = x

Now, to fill it back up, the y-intercept is 0. We know the slope is 16, so the equation is:

y = 16x

Finally, we need to find 16x = 38000. This is simple enough.

y = 16x
38000 = 16x
38000/16 = 16x/16
2375 = x