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The problem states:

- At 2:00 PM, there are 50 visitors in the museum.
- Between 2:00 PM and 4:00 PM, new visitors arrive at a rate of 2 visitors every 5 minutes.
- No visitors leave the museum during this period.

We are asked to determine how many visitors will be in the museum by 4:00 PM.

### Solution:
1. From 2:00 PM to 4:00 PM, there is a 2-hour interval, or 120 minutes.
2. The rate of new visitors is 2 visitors every 5 minutes.
   - Number of 5-minute intervals in 120 minutes = \( \frac{120}{5} = 24 \).
   - Therefore, the number of new visitors = \( 2 \times 24 = 48 \) visitors.

3. Initially, there were 50 visitors in the museum. By 4:00 PM, 48 more visitors arrive.

4. Total number of visitors at 4:00 PM = \( 50 + 48 = 98 \).

Thus, the correct answer is **98**.

Do you want further details or have any questions?

Here are five related questions to consider:
1. What would happen if the arrival rate increased to 3 visitors every 5 minutes?
2. How would the total number of visitors change if visitors could leave every 10 minutes?
3. What if the time span was extended to 5 hours instead of 2?
4. How many visitors would arrive between 3:00 PM and 4:00 PM?
5. How does the visitor count change if the initial number of visitors is doubled?

**Tip:** Always break the time into intervals when solving rate problems for accurate results.

There are 50 visitors in a museum at 2:00 P.M. Between 2 P.M. and 4 P.M., new visitors arrive at the museum at a rate of 2 visitors every 5 minutes. If no visitors leave the museum between 2 P.M. and 4 P.M., how many visitors are in the museum at 4 P.M.?

Solve a museum visitor count problem by calculating the number of visitors arriving at a constant rate. Starting with 50 visitors at 2 PM, learn how to determine how many visitors are in the museum by 4 PM using time intervals and rate calculations. Suitable for Grades 6-8.

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