The drain in your 45-gallon bathtub is partially clogged, but you need to take a shower. The shower head had a flow rate of 2.25 gallons per minute, but the bathtub only drains at a rate of 20.5 gallons per minute. What is the longest shower you can take? Round your answer to the nearest feet

Step-by-step explanation:

Given

--- Flow rate of the shower

--- Drain rate of the bathtub

-- Bathtub size

Required

Determine the maximum time of shower

First, we calculate the rate at which the bathtub fills.

The maximum time of shower is:

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11