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The Island Loop Ferry takes the same route multiple times a day. It starts at the port of Seabreeze Village and travels due south for $8$ miles to the town of Oceanview. From there, it travels due east for $15$ miles to Portlandville. Finally, it makes a straight-line journey back to Seabreeze Village. If the ferry can travel $5$ miles on a gallon of fuel, how many gallons does the ferry use to complete the route one time? If necessary, round your answer to the nearest tenth. $\newline$ ____ gallons

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Pythagorean theorem

Full solution

Q. The Island Loop Ferry takes the same route multiple times a day. It starts at the port of Seabreeze Village and travels due south for

8

miles to the town of Oceanview. From there, it travels due east for

15

miles to Portlandville. Finally, it makes a straight-line journey back to Seabreeze Village. If the ferry can travel

5

miles on a gallon of fuel, how many gallons does the ferry use to complete the route one time? If necessary, round your answer to the nearest tenth.

\newline

____ gallons

Calculate Distance Oceanview Portlandville: Calculate the distance from Oceanview to Portlandville. It's given as $15$ miles.
Calculate Distance Seabreeze Village Oceanview: Calculate the distance from Seabreeze Village to Oceanview. It's given as $8$ miles.
Use Pythagorean Theorem Portlandville Seabreeze Village: Use the Pythagorean theorem to find the distance from Portlandville back to Seabreeze Village. Let this distance be c. $\newline$ $c^2 = 8^2 + 15^2$ $\newline$ $c^2 = 64 + 225$ $\newline$ $c^2 = 289$ $\newline$ $c = \sqrt{289}$ $\newline$ $c = 17 \text{ miles}$
Add Total Distance Traveled Ferry: Add up all the distances to find the total distance traveled by the ferry. $\newline$ $\text{Total distance} = 8 \text{ miles} + 15 \text{ miles} + 17 \text{ miles}$ $\newline$ $\text{Total distance} = 40 \text{ miles}$
Calculate Fuel Usage: Calculate the fuel usage based on the ferry's fuel efficiency. $\newline$ $\text{Fuel efficiency} = 5 \text{ miles per gallon}$ $\newline$ $\text{Fuel used} = \frac{40 \text{ miles}}{5 \text{ miles per gallon}}$ $\newline$ $\text{Fuel used} = 8 \text{ gallons}$

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