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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? Round to the nearest tenth if necessary.

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pedrocarratore

Answer:

1 hour

Step-by-step explanation:

Let's assume that Patrick is travelling on a straight line throughout the whole path in order to minimize the distance.

The number of miles that he can travel on a full tank is:

[tex]m = 5\ mpg*4\ gallons\\m=20\ miles[/tex]

The distance travelled by Patrick in one hour (from 2p.m. to 3p.m.) is:

[tex]d^2=6^2+8^2\\d=\sqrt{100}\\ d=10\ miles[/tex]

If he is travelling at 10 miles per hour, and he could travel for a total of 20 miles, then the time remaining before the tank runs out of gasoline is:

[tex]t=\frac{20-10}{10}\\ t=1\ h[/tex]

If he continues at this rate, the gas will last for 1 more hour.

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