Station B is located between stations A and C. The distance from A to B is $400 ext{ km}$, and from B to C is $375 ext{ km}$. A train takes the same amount of time to travel from A to B as it does from B to C. If the train's speed between A and B is $40 ext{ km/h}$, what is the difference between the average speed of the train over the entire journey from A to C and its speed between B and C?

Question

Station B is located between stations A and C. The distance from A to B is $400 	ext{ km}$, and from B to C is $375 	ext{ km}$. A train takes the same amount of time to travel from A to B as it does from B to C. If the train's speed between A and B is $40 	ext{ km/h}$, what is the difference between the average speed of the train over the entire journey from A to C and its speed between B and C?

Accepted Answer

**Solution:**

1. Given that the time taken to travel from A to B and from B to C is the same.

2. Calculate the time taken to travel from A to B:
   - Distance = $400 	ext{ km}$
   - Speed = $40 	ext{ km/h}$
   - Time = $\frac{400}{40} = 10$ hours

3. Since the time for B to C is also 10 hours, calculate the speed for B to C:
   - Distance = $375 	ext{ km}$
   - Time = $10$ hours
   - Speed = $\frac{375}{10} = 37.5 	ext{ km/h}$

4. Calculate the average speed for the entire journey from A to C:
   - Total distance = $400 + 375 = 775 	ext{ km}$
   - Total time = $10 + 10 = 20$ hours
   - Average speed = $\frac{775}{20} = 38.75 	ext{ km/h}$

5. Find the difference between the average speed and the speed from B to C:
   - Difference = $38.75 - 37.5 = 1.25 	ext{ km/h}$

**Answer:** $1.25 	ext{ km/h}$

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