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 in 1 hour

Using the Pythagorean theorem, the distance \( d \) from the dock at 3 p.m. is \( \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \) miles. This is the distance traveled in 1 hour (from 2 p.m. to 3 p.m.).

Step2: Calculate total distance the boat can travel with full tank

The boat averages 5 miles per gallon, and the tank holds 4 gallons. So total distance \( D = 5 \times 4 = 20 \) miles.

Step3: Calculate remaining distance

Distance already traveled is 10 miles, so remaining distance \( r = 20 - 10 = 10 \) miles.

Step4: Calculate time to travel remaining distance

Since the speed is 10 miles per hour (from Step1, distance per hour is 10 miles), time \( t = \frac{10}{10} = 1 \) hour.

Answer:

1