2 A garden hose supplies 36 gallons of water in 3 minutes. Use a table of equivalent ratios to show the garden hose's water flow in gallons per minute and minutes per gallon. fow many gallons of water does the hose supply in 10 minutes? Explain.

To solve the problem, we will first determine the flow rate of the garden hose in gallons per minute and then calculate how many gallons it supplies in 10 minutes. ### Step 1: Calculate the flow rate in gallons per minute The garden hose supplies 36 gallons of water in 3 minutes. To find the flow rate in gallons per minute (GPM), we can use the formula: \[ \text{Flow Rate (GPM)} = \frac{\text{Total Gallons}}{\text{Total Minutes}} \] Substituting the known values: \[ \text{Flow Rate (GPM)} = \frac{36 \text{ gallons}}{3 \text{ minutes}} = 12 \text{ gallons per minute} \] ### Step 2: Calculate the flow rate in minutes per gallon To find the flow rate in minutes per gallon (MPG), we can take the reciprocal of the flow rate in gallons per minute: \[ \text{Flow Rate (MPG)} = \frac{1}{\text{Flow Rate (GPM)}} \] Substituting the flow rate we just calculated: \[ \text{Flow Rate (MPG)} = \frac{1}{12} \text{ minutes per gallon} \approx 0.0833 \text{ minutes per gallon} \] ### Step 3: Calculate how many gallons the hose supplies in 10 minutes Now, to find out how many gallons the hose supplies in 10 minutes, we can use the flow rate in gallons per minute: \[ \text{Gallons in 10 minutes} = \text{Flow Rate (GPM)} \times \text{Time (minutes)} \] Substituting the values: \[ \text{Gallons in 10 minutes} = 12 \text{ gallons per minute} \times 10 \text{ minutes} = 120 \text{ gallons} \] ### Summary - The garden hose supplies **12 gallons per minute**. - The flow rate is approximately **0.0833 minutes per gallon**. - In **10 minutes**, the hose supplies **120 gallons** of water. This shows that the garden hose has a consistent flow rate, allowing us to easily calculate the total amount of water supplied over any given time period.