Question

The department of transportation in each state is responsible for the improvements and repairs of that state's roads. One important job is to repaint the road lines that have worn away or faded. A painting crew is painting a 24-mile stretch of road. They have already completed a total of 9.5 miles of the road. The crew has been painting at a rate of 0.25 mile per hour and continues to paint at the same rate. Identify the two quantities that are changing in this situation, identify the independent and dependent quantities, and define the variables for these quantities. Then write an equation that relates the two quantities.

Answer 1

The independent and dependent quantities are the time spent painting and the total miles painted, respectively. The equation relating these quantities is y = 0.25x + 9.5, with x being the hours and y being the total miles painted.

Step-by-step explanation:

The two quantities that are changing in the situation where a painting crew is painting a 24-mile stretch of road and has already completed 9.5 miles at a rate of 0.25 mile per hour are the distance painted (dependent) and the time spent painting (independent). Let us define x as the independent variable representing the hours spent painting and y as the dependent variable representing the total miles painted. The equation relating the two is y = 0.25x + 9.5, where 9.5 represents the initial miles already painted.