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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.

A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance (in km) is:

This problem explores how changes in speed affect the time taken to travel a certain distance. Learn how to solve it step-by-step using algebra and the distance-speed-time relationship. Suitable for Grades 9-10.

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