The time T required to fill a pool is inversely proportional

The time T required to fill a pool is inversely proportional to the rate R at which the pump fills the pool. A particular pump can fill a pool in 15 hours when pumping at a rate of 250 gallons per hour.

A. Find the model that gives T as a funstion of R.

B. Use your model from part A to find the rate that it would take to fill the pool in 9 hours.

Solution

Let k be the constant of proportionality. Then,

A. T = k/R.

B. When T = 15, R = 250, so that 15 = k/250 or, k = 15*250 = 3750. Thus, when T = 9, we have 9 = k/R = 3750/R or, R = 3750/9 = 416.66666666 = 416.67 gallons per hour( on rounding off to 2 decimal places).