Nicky and Cristina begin running a race at the same time, though Nicky begins the race at the same time, though Nicky begins the race 36 meters ahead of Cristina. If Cristina runs at a pace of 5 meters per second and Nicky runs at a pace of only 3 meters per second, how many seconds will Nicky have run before Cristina catches up to him?

Options

A. 15 seconds
B. 18 seconds
C. 25 seconds
D. 30 seconds

Answer

To solve the problem, we need to determine how long Nicky will run before Cristina catches up to him. Here's the step-by-step solution:

### Step 1: Identify the given information
- Nicky's head start = 36 meters
- Cristina's speed = 5 meters per second
- Nicky's speed = 3 meters per second

### Step 2: Calculate the relative speed
Since both Nicky and Cristina are running in the same direction, we can find the relative speed by subtracting Nicky's speed from Cristina's speed.

\[ \text{Relative Speed} = \text{Cristina's Speed} - \text{Nicky's Speed} = 5 \, \text{m/s} - 3 \, \text{m/s} = 2 \, \text{m/s} \]

### Step 3: Use the relative speed to find the time taken for Cristina to catch up
To find the time it takes for Cristina to catch up to Nicky, we can use the formula:

\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} \]

Here, the distance is the head start that Nicky has, which is 36 meters.

\[ \text{Time} = \frac{36 \, \text{meters}}{2 \, \text{m/s}} = 18 \, \text{seconds} \]

### Step 4: Conclusion
Nicky will have run for 18 seconds before Cristina catches up to him.

### Final Answer
Nicky will have run for **18 seconds** before Cristina catches up to him.

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