Question

1. a garden hose fills a 2-gallon bucket in 5 seconds. the number of gallons, g, is proportional to the number of seconds, t, that the water is running. select all the equations that represent the relationship between g and t.

□ $g = 0.4t$
□ $t = 0.4g$
□ $g = 2.5t$
□ $t = 2.5g$
□ $g = \frac{2}{5}t$

Explanation:

Step1: Find the rate of filling

The hose fills 2 gallons in 5 seconds, so the rate is $\frac{2}{5} = 0.4$ gallons per second.

Step2: Define proportional relationship for $g$

Since $g$ (gallons) is proportional to $t$ (seconds), $g = \text{rate} \times t$, so $g = 0.4t$ or $g = \frac{2}{5}t$.

Step3: Rearrange for $t$

Solve $g = 0.4t$ for $t$: $t = \frac{g}{0.4} = 2.5g$.

Answer:

• $g = 0.4t$
• $t = 2.5g$
• $g = \frac{2}{5}t$