10 painters can paint a building in 16 hours, but because of bad weather only eight painters arrive. How long will it take them to paint the building?
The Correct Answer and Explanation is:
Correct Answer: 20 hours
To solve this problem, we use the concept of work and how it’s distributed among workers. In this case, the “work” is painting the building.
Step-by-step Explanation:
We are told that:
- 10 painters can paint a building in 16 hours.
This means that 10 painters × 16 hours = 160 painter-hours are required to complete the job.
This is the total amount of work needed: 160 painter-hours.
Now, due to bad weather, only 8 painters arrive.
Let’s calculate how long it will take 8 painters to do 160 painter-hours of work.
Let xx be the number of hours needed for 8 painters to complete the job.
We set up the equation: 8 painters×x hours=160 painter-hours8 \text{ painters} \times x \text{ hours} = 160 \text{ painter-hours}
Solving for xx: x=1608=20 hoursx = \frac{160}{8} = 20 \text{ hours}
Why This Makes Sense:
Work problems like this are based on the idea that work = number of workers × time (assuming constant work rate and efficiency). If fewer people do the job, it naturally takes more time.
Originally, 10 painters spread the workload over 16 hours. When only 8 show up, the same work (painting the whole building) must now be done by fewer people, so it takes longer.
Think of it like this: If 10 people can finish a task in a day, removing 2 people (a 20% reduction) means each of the remaining workers must do more. Since the amount of work is the same, the time needed increases proportionally.
So, with 8 painters instead of 10, it takes 20 hours instead of 16 to complete the building.
