Fuel Consumption pt. 2 (continuation)

Question

At noon one day, Corey decided to follow a straight course in a motor boat. After one hour of making no turns and traveling at a steady rate, the boat was 6 miles east and 8 miles north of its point of departure, thus, traveling 10 miles in a north east direction. After 2 hours, he travels double the distance, while maintaining his speed of 10 mph.

Assume that the fuel tank initially held 12 gallons, and that the boat gets 4 miles to the gallon. How far did Corey get before running out of fuel? When did this happen? When radioing the Coast Guard for help, how should Corey describe the boat's position?

Answer 1

the fuel tank initially held 12 gallons, and that the boat gets 4 miles to the gallon.

 

This means that in one hour (10 miles covered), 2.5 gallons are consumed.

12 gallons divided by 2.5 gallons gives the quotient 4.8, so 48 miles from the start point, the boat is out of gas.

Using trigonometry, the angle clockwise from due North of the start point is arctan 8/6, or 53 degrees east of North.