Mr. Jackson is ready to empty his backyard swimming pool for the winter. He knows that the time, T, required to empty the pool varies inversely as the rate, R, of pumping. Mr. Jackson's old pump could empty the pool in 55 minutes, pumping at a rate of 200 gallons per minute. This year he has a new pump which pumps at a rate of 325 gallons per minute. How long will it take to empty the pool this season? Round your answer to the nearest minute. DUE IN 2 HOURS, 15 POINTS, WILL GIVE BRAINLIEST.

34 minutes

Step-by-step explanation:

Given that T varies inversely as R then the equation relating them is

T = ← k is the constant of variation

To find k use the condition

T = 55 when R = 200, that is

55 = ( multiply both sides by 200 )

11000 = k, thus

T = ← equation of variation

When R = 325, then

T = ≈ 34 minutes ( to the nearest minute )

Option 2

Step-by-step explanation:

An inverse variation can be represented by the equation xy=k or y=kx .

If (x1,y1) and (x2,y2) are solutions of an inverse variation, then x1y1=k and x2y2=k

Substitute x1y1 for k

x1y1=x2y2   or x1x2=y2y1

The equation x1y1=x2y2 is called the product rule for inverse variations.

Let x be the time required, and y the rate of pumping.

x1 = 55min  y1 = 200gal/min

x2 = Unknown y2 = 325gal/min

(55)(200) = x2(325)

11,000 = x2 (325)

11,000/325 = x2

33.84 = x2

34 minutes

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