Question

The fuel gauge in Nic’s car says that he has 26 miles to go until his tank is empty. He passed a fuel station 19 miles ago, and a sign says there is a town only 8 miles ahead. If he takes a chance and drives ahead to the town and there isn’t a fuel station there, does he have enough fuel to go back to the last station? Include a diagram along a number line, and use absolute value to find your answer.

Answer 1

Answer: No

Step-by-step explanation:

First, we know Nic's Car has 26 miles worth on gas. This is the total distance he can travel before running out.

Total Gas = 26 miles

Nick is in the middle of the road, 8 miles from a town and 19 miles from a Gas Station on the opposite direction. We can write down those distances like:

Distance's to Town (Dt) = 8 miles

Distance's to Gas Station (Dgs) = -19 miles

Because the Gas station is on the reverse direction of the town, we write down the distance on negative.

In the case we are studing, Nick decides to go to the town but he does not find a Gas Station so he need to turn back to the Gas Station. Nick's Travel will be divided on 3 parts:

First, Nick travel from where he is (the origin) to the town, this distance is 8 miles.

Second, he will return from the town to the origin point, distance is un opositte direction to the town so is equal to -8 miles.

Third, from here, he will travel to the Gas Station, this distance is -19 miles as previously stated.

We can sum the magnitudes of this distances to know if the Gas Tank can take, the distance should be less than 26 miles.

Total Travel = Dt + |-Dt| + | Dgs |

Total Travel = 8 miles + 8 miles + 26 miles

Total Travel = 42 miles

This distance is much larger than 26 miles, which means the Gas Fuel will be out before reaching the Gas Station