Question

the rational function $y = \frac{19,800}{x}$ models the time, in hours, needed to fill a swimming pool, where $x$ is the flow rate of the hose, in gallons per hour.

three hoses – two with a flow rate of 400 gal/hr and one with a flow rate of 300 gal/hr – are used to fill the pool. what is the total flow rate if all three hoses are used?

$\boldsymbol{\quad}$ gal/hr

if the three hoses are used to start filling the pool at 10 a.m. on tuesday, when will the pool be completely filled?

$\boldsymbol{\quad}$

Explanation:

Step1: Calculate total flow rate

Two hoses at 400 gal/hr: \(2\times400 = 800\) gal/hr. One hose at 300 gal/hr. Total: \(800 + 300 = 1100\) gal/hr.

Step2: Find time to fill pool

Use \(y=\frac{19800}{x}\), \(x = 1100\). So \(y=\frac{19800}{1100}=18\) hours.

Step3: Determine completion time

Start at 10 a.m. Tuesday. 18 hours later: 10 a.m. + 18 hours = 4 a.m. Wednesday.

Answer:

Total flow rate: 1100 gal/hr
Completion time: 4 a.m. on Wednesday