a garden hose fills a 2 - gallon bucket in 5 seconds. the number of gallons, g, is proportional to the…

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

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

Answer

Explanation:

Step1: Find the rate of filling

The hose fills (2) gallons in (5) seconds. The rate of filling (gallons per second) is (\frac{g}{t}). Using the values (g = 2) and (t=5), the rate (k=\frac{2}{5}=0.4). The general equation for a proportional relationship is (g = kt), so (g = 0.4t). Also, from (g = 0.4t), we can solve for (t): (t=\frac{g}{0.4}=\frac{10g}{4}=2.5g). And (\frac{2}{5}=0.4), so (g=\frac{2}{5}t) is equivalent to (g = 0.4t).

Answer:

(g = 0.4t), (t = 2.5g), (g=\frac{2}{5}t)