Question

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1. patrick has a gas-powered boat that averages 5 miles per gallon of gasoline, and the tank holds 4 gallons. at 2 p.m., he left the dock. at 3 p.m., he was 6 miles west and 8 miles south of the dock. if he continues at this rate, in how many more hours will the tank be out of gasoline?

Explanation:

Step1: Calculate distance traveled

Use Pythagorean theorem:
$$\text{Distance} = \sqrt{6^2 + 8^2} = \sqrt{36+64} = \sqrt{100} = 10 \text{ miles}$$

Step2: Find time elapsed

Time between 2-3 p.m. is 1 hour.

Step3: Calculate gas used per hour

Gas rate: $\frac{1 \text{ gallon}}{5 \text{ miles}}$. Gas used in 1 hour:
$$10 \text{ miles} \times \frac{1 \text{ gallon}}{5 \text{ miles}} = 2 \text{ gallons}$$

Step4: Find remaining gas and time

Remaining gas: $4 - 2 = 2$ gallons. Time left:
$$2 \text{ gallons} \times \frac{5 \text{ miles}}{1 \text{ gallon}} \times \frac{1 \text{ hour}}{10 \text{ miles}} = 1 \text{ hour}$$

Answer:

1 hour