Question

1. the time it takes to fill a water tank varies inversely with the water rate of the hose. at 8 gallons per minute, a hose can fill the tank in 45 minutes. how long will it take to fill the same tank at 15 gallons per minute?

Explanation:

Step1: Define inverse variation formula

Inverse variation: $t = \frac{k}{r}$, where $t$ = time, $r$ = rate, $k$ = constant.

Step2: Solve for constant $k$

Substitute $t=45$, $r=8$:
$45 = \frac{k}{8}$
$k = 45 \times 8 = 360$

Step3: Find time at $r=15$

Use $k=360$, $r=15$:
$t = \frac{360}{15}$

Answer:

24 minutes