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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

Answer :

MrRoyal

Answer:

[tex]Time = 1.978\ min[/tex]

Step-by-step explanation:

Given

[tex]R_1 = 2.25\ gal/min[/tex] --- Flow rate of the shower

[tex]R_2 = 20.5\ gal/min[/tex] --- Drain rate of the bathtub

[tex]Size = 45gal[/tex] -- Bathtub size

Required

Determine the maximum time of shower

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

[tex]R_3 = R_1 + R_2[/tex]

[tex]R_3 = 2.25 + 20.5[/tex]

[tex]R_3 = 22.75gal/min[/tex]

The maximum time of shower is:

[tex]Time = \frac{Size}{R_3}[/tex]

[tex]Time = \frac{45gal}{22.75gal/min}[/tex]

[tex]Time = 1.978\ min[/tex]  

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