2440.52 – Wilbur's Boat Trip

On a full tank, Wilbur’s speedboat can run 4 hours at full throttle or 7 hours at half throttle. It happens that yesterday he and his brother Orville went downstream from Dayton to Moraine OH starting with a full tank. It took one hour at full throttle. They returned at half throttle, and it took 3 hours. When they re-filled the tank, it took 3.8 gallons. Orville claimed that Wilbur should then be able to calculate the capacity of the tank. Wilbur succeeded. What did he do?

Solution

The one hour downriver trip used $\dfrac{1}{4}$ of a tank. The way back used $\dfrac{3}{7}$ of a tank. Total fuel consumed was $3.8$ gallons. So,

$\dfrac{t}{4} + \dfrac{3t}{7} = 3.8$

where $t$ is the capacity of the tank. Solving this equation, we find

$\begin{aligned}\dfrac{7t + 12t}{28} &= 3.8 \\19t &= 28 3.8 = 106.4 \\t &= 5.6 \text{ gallons}\end{aligned}$

That's a reasonable size tank for a small boat. Google "speedboat gas tank size" for more information.

(We can hope that the gas is diesel, which is safer to handle than regular gasoline. Thanks to David Fuller for this fact.)