Final answer:
Joan must travel at a rate of 0.2 miles per minute to cover 9 miles in 45 minutes. This is confirmed by checking the reasonability of the answer, as 0.2 miles per minute equates to a very reasonable cycling speed of 12 miles per hour.
Step-by-step explanation:
Joan plans to ride 9 miles in 45 minutes. To calculate the rate at which Joan must travel, we simply divide the total distance by the total time. The rate can be calculated as folows:
RATE (miles per minute) = DISTANCE (miles) / TIME (minutes)
In Joan's case:
RATE = 9 miles / 45 minutes
RATE = 0.2 miles per minute
Therefore, Joan must travel at a rate of 0.2 miles per minute to cover 9 miles in 45 minutes.
Step 2 involves checking if the answer is reasonable. We know that a pace of 0.2 miles per minute is equivalent to 12 miles per hour (because 0.2 miles per minute * 60 minutes in an hour equals 12). This pace is a reasonable cycling speed, confirming that our calculation is likely correct.