Final answer:
Michelle was running at a speed of 6 miles per hour. This was calculated using the relationships between the distances they ran and the time taken, considering that Kevin runs 3 miles per hour faster than Michelle.
Step-by-step explanation:
To find out how fast Michelle was running, we can use the information provided about the distances Kevin and Michelle ran, as well as their relative speeds.
Let's denote Michelle's speed as M miles per hour. According to the data, Kevin runs at a speed of M + 3 miles per hour (since he is 3 miles per hour faster than Michelle). If both Kevin and Michelle run for the same amount of time, we can use their speeds to express this relationship.
For Kevin, who ran 6 miles, time can be represented as 6 / (M + 3) hours. For Michelle, who ran 4 miles, time can be represented as 4 / M hours. Since the times are equal, we can set the two expressions equal to each other:
6 / (M + 3) = 4 / M
By cross-multiplying, we get:
6M = 4(M + 3)
6M = 4M + 12
6M - 4M = 12
2M = 12
M = 6
Therefore, Michelle's speed was 6 miles per hour.