Question

Brain is driving along a straight highway. His truck can travel 22 miles per gallon of gasoline,
and it has 2 gallons of gas remaining. On the map the truck’s current location is (7,12), and the
nearest gas station on the highway is located at (16,52). Each unit on the map represents 1 mile.
Will the truck reach the gas station before running out of gas? Support your answer.

Answer 1

To determine if Brain’s truck can reach the gas station before running out of gas, we first need to calculate how far the truck can travel with the remaining gasoline.

Since the truck travels 22 miles per gallon and has 2 gallons of gas left, the total distance the truck can travel is:

\[
22 \text{ miles/gallon} \times 2 \text{ gallons} = 44 \text{ miles}
\]

Next, we need to calculate the distance from the truck's current location (7,12) to the gas station located at (16,52). We will use the distance formula to find this distance:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Substituting the coordinates of the truck and the gas station into the formula:

\[
d = \sqrt{(16 - 7)^2 + (52 - 12)^2}
\]
\[
= \sqrt{(9)^2 + (40)^2}
\]
\[
= \sqrt{81 + 1600}
\]
\[
= \sqrt{1681}
\]
\[
= 41 \text{ miles}
\]

Now, we compare the distance to the gas station (41 miles) and the maximum distance the truck can travel (44 miles).

Since 41 miles is less than 44 miles, the truck can reach the gas station before running out of gas.

**Conclusion: Yes, the truck will reach the gas station before running out of gas.**