Question

the table below shows how the number of hours needed to fill a pool depends on the flow rate of the hoses to fill it.

flow rate, x (gal/hr)	time, y (hours)
45	400
36	500
30	600

how long will it take to fill the pool if two hoses are used, one that fills at a rate of 40 gallons per hour and one that fills at a rate of 60 gallons per hour?

○ 100 hours
○ 150 hours
○ 180 hours
○ 200 hours

Explanation:

Step1: Find pool total volume

Calculate using any $(x,y)$ pair: $V = x \times y$. Using $x=60, y=300$:
$V = 60 \times 300 = 18000$ gallons

Step2: Find combined flow rate

Add the two hoses' rates:
$x_{total} = 40 + 60 = 100$ gal/hr

Step3: Calculate total time

Time = $\frac{\text{Total Volume}}{\text{Combined Rate}}$
$t = \frac{18000}{100}$

Answer:

180 hours (Option: 180 hours)