Question

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.

Answer 1

1 hour

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:

`m = 5\ mpg*4\ gallons\\m=20\ miles`

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

`d^2=6^2+8^2\\d=√(100)\\ d=10\ miles`

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:

`t=(20-10)/(10)\\ t=1\ h`

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