Question

Carlos was driving at a constant speed. After 3 hours, he was 300 miles from a town on the highway. After 6 hours, he was 480 miles from the town. Which function represents Carlos' distance, y, from the town after x hours?

Answer 1

Carlos' distance from the town after x hours can be represented by the function y = 60x + 120.

Step-by-step explanation:

The distance, y, from the town after x hours can be represented by a linear function. Let's calculate the rate of change of distance with respect to time. After 3 hours, Carlos traveled 300 miles, and after 6 hours, he traveled 480 miles. The rate of change of distance is the difference in distance divided by the difference in time, which is (480 - 300) / (6 - 3) = 180 / 3 = 60 miles per hour. This means that Carlos was traveling at a constant speed of 60 miles per hour.

To find the function that represents Carlos' distance from the town after x hours, we can use the formula y = mx + b, where m is the rate of change (slope) and b is the initial distance from the town. Since Carlos was 300 miles from the town after 3 hours, we can substitute these values into the equation: 300 = 60 * 3 + b. Solving for b, we get b = 300 - 180 = 120. Therefore, the function that represents Carlos' distance from the town after x hours is y = 60x + 120.