Ram and Rahim standing at a distance of 680m run towards each other at a speed of 8m/sec and 9m/sec respectively. After how long will they meet ?
A. 17 sec
B. 24 sec
C. 40 sec
D. 36 sec

Options

A. B
B. A
C. D
D. C

Answer

To solve the problem of when Ram and Rahim will meet while running towards each other, we can follow these steps:

### Step 1: Understand the Problem
Ram and Rahim are initially 680 meters apart. Ram runs at a speed of 8 meters per second, and Rahim runs at a speed of 9 meters per second. We need to find out how long it will take for them to meet.

### Step 2: Calculate the Relative Speed
Since both Ram and Rahim are running towards each other, we can add their speeds to find the relative speed.

- Speed of Ram = 8 m/s
- Speed of Rahim = 9 m/s

**Relative Speed = Speed of Ram + Speed of Rahim**
\[ \text{Relative Speed} = 8 \, \text{m/s} + 9 \, \text{m/s} = 17 \, \text{m/s} \]

### Step 3: Use the Formula for Time
We can use the formula for time, which is derived from the formula for speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Rearranging this gives us:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

### Step 4: Substitute the Values
Now we can substitute the distance and the relative speed into the formula for time.

- Distance = 680 meters
- Relative Speed = 17 m/s

**Time = \(\frac{680 \, \text{meters}}{17 \, \text{m/s}}\)**

### Step 5: Calculate the Time
Now we perform the division:
\[ \text{Time} = \frac{680}{17} = 40 \, \text{seconds} \]

### Conclusion
Ram and Rahim will meet after **40 seconds**.

### Answer
C. 40 sec

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