A car traveling on a highway is 60 miles away from home after 1 hour, and is 300 miles away from home after 5 hours. What is the rate of change of the car’s distance over time?
60/1 = 60 miles/hour
300/5 = 60 miles/hour
sure looks like 60 miles/hour
To calculate the rate of change of the car's distance over time, we need to find the average speed of the car. Average speed can be calculated by dividing the change in distance by the change in time.
In this case, the car's distance changes from 60 miles to 300 miles, which is a total change of 300 - 60 = 240 miles.
The time it takes for this change to occur is from 1 hour to 5 hours, which is a total change of 5 - 1 = 4 hours.
To find the rate of change, we can divide the change in distance (240 miles) by the change in time (4 hours):
Rate of change = Change in distance / Change in time
= 240 miles / 4 hours
= 60 miles per hour (mph)
Therefore, the rate of change of the car's distance over time is 60 miles per hour.