Final answer:
To determine Jim and Joanne's speeds, equations based on their commute distances and the fact that Jim travels 5 mph slower were set up. The calculated speeds were 15 mph for Jim and 20 mph for Joanne, which do not match any of the provided options, indicating a potential mistake in the question or choices.
Step-by-step explanation:
To solve the problem, we must set up equations based on the fact that Jim and Joanne take the same amount of time to get to work, but Jim travels 5 mph slower than Joanne.
Let x represent Joanne's speed in mph. Then, Jim's speed will be x - 5 mph. Since they take the same time to commute, we know that Time = Distance ÷ Speed. For Jim, the time is equal to 30 ÷ (x - 5), and for Joanne, the time is equal to 40 ÷ x. Setting these two expressions equal gives us the equation:
30 ÷ (x - 5) = 40 ÷ x
By cross-multiplying, we have:
30x = 40(x - 5)
30x = 40x - 200
Now, solve for x:
-10x = -200
x = 20 mph
Joanne's speed is 20 mph. Therefore, Jim's speed is 20 - 5 = 15 mph. However, none of the options provided match these speeds, which imply there might be an error in the provided choices or in the initial information given in the question.