Let's solve the problem:

The problem involves finding the distance a man traveled, given that changes in his speed result in changes in the time taken.

Let:

• $d$ be the distance (in km),
• $s$ be the original speed (in km/h),
• $t$ be the original time (in hours).

From the problem:

1. If the man increased his speed by 3 km/h, the time taken would decrease by 40 minutes (or $\frac{2}{3}$ hours): $\frac{d}{s + 3} = t - \frac{2}{3}$

2. If the man decreased his speed by 2 km/h, the time taken would increase by 40 minutes (or $\frac{2}{3}$ hours): $\frac{d}{s - 2} = t + \frac{2}{3}$

We can also express the original time as: $t = \frac{d}{s}$

Now, let's solve these equations to find the distance $d$.

Starting from the first equation, we can equate the expression for $t$ from both equations and simplify to find $d$.

Let me calculate this.The solution shows that the distance $d$ is 40 km and the original speed $s$ is 12 km/h.

Thus, the correct answer is $\boxed{40}$ km (option D).

Would you like more details or have any questions?

Here are some related questions you might consider:

1. How would the problem change if the man reduced his speed by 3 km/h instead of 2 km/h?
2. What if the increase in speed was 5 km/h, how would the time difference change?
3. How can you derive the relationship between speed and time for different distances?
4. What happens if the time difference were 1 hour instead of 40 minutes?
5. How can you check the accuracy of this solution using a graph?

Tip: When working with speed, time, and distance, always remember that $\text{Distance} = \text{Speed} \times \text{Time}$. Adjusting one of these variables will directly affect the others.