Jack jogs around a race course that is 3 miles long. He takes 20 minutes to complete the first lap and 25 minutes to complete the second lap. What is his average speed in miles per hour for the entire jog?

Introduction:
This question is about average speed over a trip where the speeds (or times) over different segments are not the same. It is important to remember that average speed is total distance divided by total time, not the average of individual speeds or times.

Given Data / Assumptions:

• Length of one lap around the course = 3 miles.
• Time for first lap = 20 minutes.
• Time for second lap = 25 minutes.
• Jack runs two laps in total.
• We must find his average speed in miles per hour.

Concept / Approach:
Average speed is always:
Average speed = Total distance / Total timeWe must be careful to convert total time into hours because the answer is required in miles per hour (mph).

Step-by-Step Solution:
Step 1: Compute total distance.Each lap is 3 miles, and he runs 2 laps.Total distance = 2 * 3 = 6 miles.Step 2: Compute total time in minutes.Total time = 20 minutes + 25 minutes = 45 minutes.Step 3: Convert total time to hours.45 minutes = 45 / 60 hours = 0.75 hours.Step 4: Apply the average speed formula.Average speed = Total distance / Total timeAverage speed = 6 miles / 0.75 hours = 8 mph

Verification / Alternative check:
You can check by proportion: if he travelled 8 miles in 1 hour, then in 0.75 hours he would travel 8 * 0.75 = 6 miles, which matches the actual total distance. This confirms that 8 mph is consistent with the given data.

Why Other Options Are Wrong:
6 mph: Would imply a distance of 6 * 0.75 = 4.5 miles in 0.75 hours, which is too small.
9 mph: In 0.75 hours, 9 mph would cover 6.75 miles, larger than 6 miles.
10 mph: Would correspond to 7.5 miles in 0.75 hours, again incorrect.
7 mph: In 0.75 hours, distance would be 5.25 miles, not 6 miles.

Common Pitfalls:
Students sometimes average times or incorrectly average hypothetical speeds per lap. The correct method is always to sum total distance and total time first, then divide. This is critical when segment times or speeds differ.

Final Answer:
Jack's average speed for the whole jog is 8 mph.