To solve the problem step by step, let's break it down:
### Step 1: Understand the Initial Conditions
- The thief is initially 50 meters ahead of the police.
- After 10 seconds, the distance between them reduces by 6 meters.
**Hint:** Identify the initial distance and the change in distance over the given time.
### Step 2: Calculate the Distance After 10 Seconds
- The initial distance is 50 meters.
- The distance reduced in 10 seconds is 6 meters.
- Therefore, the new distance after 10 seconds is:
\[
\text{New Distance} = \text{Initial Distance} - \text{Distance Reduced} = 50 \, \text{m} - 6 \, \text{m} = 44 \, \text{m}
\]
**Hint:** Use subtraction to find the new distance after the reduction.
### Step 3: Determine the Remaining Time
- The total time we are interested in is 25 seconds.
- Since 10 seconds have already passed, the remaining time is:
\[
\text{Remaining Time} = 25 \, \text{s} - 10 \, \text{s} = 15 \, \text{s}
\]
**Hint:** Subtract the elapsed time from the total time to find the remaining time.
### Step 4: Calculate the Speed of the Police Relative to the Thief
- The relative distance reduced in 10 seconds is 6 meters.
- Therefore, the speed of the police relative to the thief is:
\[
\text{Speed} = \frac{\text{Relative Distance}}{\text{Time}} = \frac{6 \, \text{m}}{10 \, \text{s}} = 0.6 \, \text{m/s}
\]
**Hint:** Use the formula for speed, which is distance divided by time.
### Step 5: Calculate the Relative Distance in the Remaining Time
- Now, we need to find out how much distance the police will cover relative to the thief in the remaining 15 seconds:
\[
\text{Relative Distance} = \text{Speed} \times \text{Time} = 0.6 \, \text{m/s} \times 15 \, \text{s} = 9 \, \text{m}
\]
**Hint:** Multiply the speed by the remaining time to find the distance covered.
### Step 6: Calculate the Final Distance Between the Police and the Thief
- The distance after 10 seconds was 44 meters. Now, we need to reduce this distance by the relative distance of 9 meters:
\[
\text{Final Distance} = \text{Distance After 10s} - \text{Relative Distance} = 44 \, \text{m} - 9 \, \text{m} = 35 \, \text{m}
\]
**Hint:** Subtract the relative distance from the distance after 10 seconds to find the final distance.
### Conclusion
The distance between the police and the thief after 25 seconds is **35 meters**.
**Final Answer:** 35 meters.
