Let's break this down step by step.

Step 1: Determine the total work in painter-hours

From the problem, we know:

• Last year, 3 painters took 8 hours to complete the job.

Thus, the total work required is: $3 \times 8 = 24 \text{ painter-hours}$

Step 2: Calculate the time required with 5 painters

• This year, 5 painters will be working.
• Since the total work remains the same (24 painter-hours), the time required is: $\frac{24 \text{ painter-hours}}{5 \text{ painters}} = 4.8 \text{ hours}$

Converting 4.8 hours into hours and minutes: $0.8 \times 60 = 48 \text{ minutes}$ So, the painting will take 4 hours 48 minutes.

Step 3: Find the finishing time

• They start at 09:30.
• Work duration is 4 hours 48 minutes.
• Adding this to 09:30:

$09:30 + 4:48 = 14:18$

Step 4: Account for the 40-minute break

• Including the 40-minute break, we add:

$14:18 + 0:40 = 14:58$

Final Answer:

The painters will finish at 14:58 (2:58 PM).

Would you like a more detailed explanation of any step?

Here are some related questions to expand on this topic:

1. If only 2 painters were available this year, how long would it take?
2. How much time would be saved if 6 painters worked instead of 5?
3. What if the painters took two 20-minute breaks instead of one 40-minute break?
4. How long would it take if each painter worked at 90% efficiency?
5. If they started at 08:00 instead, what would the new finishing time be?

Tip: When working with time calculations, always convert fractional hours into minutes to avoid miscalculations!