Two girls move in opposite directions, one from A to B and other from B to A. The girl from A reaches the destination in 16 hrs and girl from B reaches her destination in 25 hrs, after having met. If former's speed is 25 km/hr, what will be the speed of latter?

Let's denote:

- The speed of the girl starting from A as \( S_A = 25 \, \text{km/hr} \)
- The speed of the girl starting from B as \( S_B \, \text{(km/hr)} \)
- The time taken by the girl from A to meet the girl from B as \( t_A \, \text{(hrs)} \)
- The time taken by the girl from B to meet the girl from A as \( t_B \, \text{(hrs)} \)

From the problem, we know:

- The total time taken by the girl from A to reach her destination is \( 16 \, \text{hrs} \), so the time taken by her to meet the girl from B is \( t_A = 16 \, \text{hrs} \).
- The total time taken by the girl from B to reach her destination is \( 25 \, \text{hrs} \), so the time taken by her to meet the girl from A is \( t_B = 25 \, \text{hrs} \).

Since the two girls move in opposite directions and meet at some point, the total distance traveled by both girls is the same. Therefore, the total distance \( D \) can be expressed as:

\[
D = S_A \cdot t_A = S_B \cdot t_B
\]

Substitute the given values:

\[
25 \cdot 16 = S_B \cdot 25
\]

Now, solve for \( S_B \):

\[
S_B = \frac{25 \cdot 16}{25} = 16 \, \text{km/hr}
\]

Thus, the speed of the girl starting from B is \( 16 \, \text{km/hr} \).

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Would you like more details or have any questions? 

Here are five related questions for further practice:

1. What is the total distance between points A and B?
2. If both girls had started at the same time, when would they meet?
3. What would be the relative speed of the two girls?
4. How much distance does the girl from A cover before meeting the other girl?
5. If the speed of the girl from A were 30 km/hr, how would that affect the meeting time?

**Tip**: When solving problems with two objects moving towards each other, remember that their relative speed is the sum of their individual speeds.

Two girls move in opposite directions, one from A to B and the other from B to A. The girl from A reaches the destination in 16 hrs and the girl from B reaches her destination in 25 hrs, after having met. If the former's speed is 25 km/hr, what will be the speed of the latter?

Solve this relative motion problem where two girls move in opposite directions and meet at a point. One girl's speed is given as 25 km/hr, and the solution involves calculating the speed of the other girl. Suitable for Grades 9-10, this problem covers key concepts like speed, time, and uniform motion.

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