Final answer:
Quinn's walking speed is 6 miles per hour. By setting up and solving an equation based on the times and the constant track distance, we find that Quinn walks at a rate 2 miles per hour slower than the running speed.
Step-by-step explanation:
To determine at what rate Quinn is walking, we need to compare the time it takes for Quinn to walk and run around the track. Since Quinn walks the track in 20 minutes and runs around the track in 15 minutes, and we're told that Quinn runs at a speed that is 2 miles per hour faster than walking, we can set up an equation to solve for the walking speed.
Let's define Quinn's walking speed as x miles per hour. Therefore, Quinn's running speed would be x + 2 mph. Given that time equals distance divided by speed, we can use the times provided to create the following equations, assuming the track's distance is the same for walking and running:
- Time walking: 20 minutes = 20 / 60 hours = 1/3 hours
- Time running: 15 minutes = 15 / 60 hours = 1/4 hours
Now, we set up our equations based on the fact that distance = speed × time:
- Walk distance: x × (1/3) = Track distance
- Run distance: (x + 2) × (1/4) = Track distance
Since the track distance is the same for both walking and running, we set the two equations equal to each other:
x × (1/3) = (x + 2) × (1/4)
Solving for x, we get:
1/3x = 1/4x + 1/2
To clear the fractions, multiply everything by 12 (the lowest common denominator):
4x = 3x + 6
Subtract 3x from both sides:
x = 6
Thus, Quinn's walking speed is 6 mph, which corresponds to option (a).