The problem in the image can be summarized as follows:

A cyclist traveled a certain distance over three days.

• On the first day, he traveled 40% of the total distance.
• On the second day, he traveled 45% of the remaining distance.
• On the third day, he traveled the remaining 66 km.

We need to determine the total distance the cyclist traveled over the three days.

Solution:

Let the total distance be $D$ km.

1. Day 1: The cyclist covers 40% of the total distance.
   So, after the first day, the remaining distance is:
   $D - 0.40D = 0.60D$.

2. Day 2: The cyclist covers 45% of the remaining distance (which is $0.60D$).
   The distance covered on the second day is:
   $0.45 \times 0.60D = 0.27D$.
   After the second day, the remaining distance is:
   $0.60D - 0.27D = 0.33D$.

3. Day 3: The cyclist covers the remaining distance, which is 66 km.
   Therefore,
   $0.33D = 66$.

Solving for $D$:

$D = \frac{66}{0.33} = 200 \, \text{km}$

So, the total distance the cyclist traveled over the three days is 200 km.

Would you like a detailed explanation of any step? Here are some related questions for practice:

1. What percentage of the total distance did the cyclist cover on the third day?
2. How many kilometers did the cyclist travel on the second day?
3. What is the total distance covered in the first two days?
4. If the cyclist traveled 10% faster each day, how would this affect the distance covered each day?
5. How long would it take the cyclist to cover 300 km using the same daily percentage distribution?

Tip: Always break down percentage-based problems step by step to avoid confusion when dealing with multiple days or stages.