Question

A new food delivery robot on a college campus is doing test runs at a constant speed of 4 miles per hour. The average test run is 3 miles from the campus cafeteria but varies a distance of 1.5 miles more or less than that. If x is the number of hours the robot is performing a test run, the equation that can be used to find the minimum and maximum time (in hours) for a test run is ?

Answer 1

The minimum and maximum time for the food delivery robot's test runs are found using the equations x_min = (3 - 1.5 miles) / 4 miles/hour for the minimum distance and x_max = (3 + 1.5 miles) / 4 miles/hour for the maximum distance, resulting in 0.375 hours and 1.125 hours respectively.

Step-by-step explanation:

The equation we need will help us find the minimum and maximum time (x) for a test run of the food delivery robot. Given that the robot's speed is 4 miles per hour, and the average distance for a test run is 3 miles (with a variation of 1.5 miles more or less), we can represent the time taken for the run in terms of distance and speed.

To find x, the time in hours, we use the formula:

Time (x) = Distance / Speed

For the minimum distance (3 - 1.5 miles), the equation for time will be:

xmin = (3 - 1.5) miles / 4 miles/hour = 1.5 / 4 hours

For the maximum distance (3 + 1.5 miles), the equation for time will be:

xmax = (3 + 1.5) miles / 4 miles/hour = 4.5 / 4 hours

So, to calculate the time it takes for the minimum and maximum test runs we perform the divisions:

xmin = 0.375 hours (Minimum Time)

xmax = 1.125 hours (Maximum Time)