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To solve the problem, we need to calculate the total number of 20-minute slots available for the computers in one day.

### Step 1: Determine total time the library is open

The library is open in two sessions:

1. **Morning session**: From 09:15 to 12:30
2. **Afternoon session**: From 13:15 to 16:30

We also know the computers cannot be booked for the final 25 minutes of the day.

#### Morning session duration:
- The library opens at 09:15 and closes at 12:30.
- The time difference is: \(12:30 - 09:15 = 3\) hours and 15 minutes.
- In minutes: \(3 \times 60 + 15 = 195\) minutes.

#### Afternoon session duration:
- The afternoon session is from 13:15 to 16:30.
- The time difference is: \(16:30 - 13:15 = 3\) hours and 15 minutes.
- In minutes: \(3 \times 60 + 15 = 195\) minutes.

### Step 2: Exclude the final 25 minutes
The library closes for computer checks in the final 25 minutes of the day. Thus, we exclude this from the total open time.

### Step 3: Calculate total available time for bookings
The total time in both sessions is:
\[
195 \, \text{(morning)} + 195 \, \text{(afternoon)} = 390 \, \text{minutes}
\]
Excluding 25 minutes for checks:
\[
390 - 25 = 365 \, \text{minutes available for bookings.}
\]

### Step 4: Determine the number of 20-minute slots
Now, we calculate how many 20-minute slots fit into 365 minutes:
\[
\frac{365}{20} = 18 \, \text{slots} \, \text{(quotient)}.
\]

### Step 5: Multiply by the number of computers
The library has 5 computers, so the total number of slots is:
\[
18 \times 5 = 90 \, \text{slots}.
\]

Thus, the maximum number of 20-minute slots that could be booked in one day is **90 slots**.

Would you like more details or further clarification?

Here are 5 related questions to explore further:
1. How would the number of slots change if the library reduced its afternoon hours?
2. What if the time slot was changed to 30 minutes instead of 20 minutes?
3. How many slots would be available if the library had only 3 computers?
4. How would the results change if the final 25 minutes were reduced to 15 minutes?
5. What if each session was reduced by 30 minutes?

**Tip**: Breaking a problem into smaller parts helps ensure accuracy in complex scenarios.

A public library has 5 computers, each of which can be booked for 20-minute slots. The library is open from 09:15 to 12:30 and from 13:15 to 16:30 each day. The computers are checked in the final 25 minutes of the day and cannot be booked during that time. What is the maximum number of 20-minute slots that could be booked in one day?

Calculate the maximum number of 20-minute slots for 5 computers in a public library open from 09:15 to 12:30 and 13:15 to 16:30, excluding the final 25 minutes of the day. Step-by-step breakdown of available booking slots and total bookings.

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