Questions: Abdul and Justin are driving separate cars to New York. They begin the trip with full gas tanks. The amount of gas (in gallons) remaining in the tank of each car depends on the number of miles driven, as shown below.

Abdul and Justin are driving separate cars to New York. They begin the trip with full gas tanks. The amount of gas (in gallons) remaining in the tank of each car depends on the number of miles driven, as shown below.

Transcript text: Abdul and Justin are driving separate cars to New York. They begin the trip with full gas tanks. The amount of gas (in gallons) remaining in the tank of each car depends on the number of miles driven, as shown below.

Solution

Solution Steps

Step 1: Find the equation for Justin's car

The graph for Justin's car is a straight line passing through the points (0, 18) and (6, 6). The slope of the line is given by: \(m = \frac{6-18}{6-0} = \frac{-12}{6} = -2\) The y-intercept is 18. So the equation for Justin's car is: \(y = -2x + 18\)

Step 2: Find the equation for Abdul's car

The graph for Abdul's car is a straight line passing through the points (0, 14) and (9, 0). The slope of the line is given by: \(m = \frac{0-14}{9-0} = \frac{-14}{9}\) The y-intercept is 14. So the equation for Abdul's car is: \(y = -\frac{14}{9}x + 14\)

Step 3: Find the point of intersection

The lines intersect where the amount of gas remaining is the same for both cars. We set the two equations equal to each other and solve for \(x\): \(-2x + 18 = -\frac{14}{9}x + 14\) Multiply both sides by 9: \(-18x + 162 = -14x + 126\) \(162 - 126 = 18x - 14x\) \(36 = 4x\) \(x = 9\)

Substituting \(x = 9\) into Justin's equation: \(y = -2(9) + 18\) \(y = -18 + 18\) \(y = 0\) So the point of intersection is (9, 0).