If 4 painters can paint 3 rooms in 12 hours, how long will it take for:
a) 1 painter to paint 3 rooms?
b) 1 painter to paint 1 room?
c) 4 painters to paint 1 room?
d) 2 painters to paint 6 rooms
To solve this problem, we can set up a proportion using the given information. Let's start with the given information: 4 painters can paint 3 rooms in 12 hours.
a) To find out how long it will take for 1 painter to paint 3 rooms, we can use the proportion: 4 painters / 12 hours = 1 painter / x hours.
Cross-multiplying, we get: 4 painters * x hours = 12 hours * 1 painter.
Simplifying, we have: 4x = 12.
Dividing both sides by 4, we get: x = 3.
Therefore, it will take 1 painter 3 hours to paint 3 rooms.
b) To find out how long it will take for 1 painter to paint 1 room, we can set up a new proportion: 4 painters / 12 hours = 1 painter / x hours.
Using the same steps as before, we get: 4x = 12.
Dividing both sides by 4, we get: x = 3.
Therefore, it will take 1 painter 3 hours to paint 1 room.
c) To find out how long it will take for 4 painters to paint 1 room, we can set up a new proportion: 4 painters / 12 hours = 1 painter / x hours (since we are looking for the time it takes for 4 painters to paint 1 room).
Using the same steps as before, we get: 4x = 12.
Dividing both sides by 4, we get: x = 3.
Therefore, it will take 4 painters 3 hours to paint 1 room.
d) To find out how long it will take for 2 painters to paint 6 rooms, we can set up a new proportion: 4 painters / 12 hours = 2 painters / x hours (since we are looking for the time it takes for 2 painters to paint 6 rooms).
Using the same steps as before, we get: 4x = 12 * 2.
Simplifying, we have: 4x = 24.
Dividing both sides by 4, we get: x = 6.
Therefore, it will take 2 painters 6 hours to paint 6 rooms.
To find the answers to these questions, we can use the concept of work rate. The work rate is the amount of work done per unit of time. In this case, the work rate will be measured in rooms per hour.
Given that 4 painters can paint 3 rooms in 12 hours, we can first calculate the work rate of the 4 painters.
Work rate of 4 painters = (Number of rooms) / (Number of hours) = 3 rooms / 12 hours = 1/4 rooms per hour
Now, we can use this work rate to solve the following questions:
a) 1 painter to paint 3 rooms:
Since 4 painters can complete the work in 12 hours, we can assume that 1 painter will take 4 times longer to complete the same amount of work. Therefore, it will take 12 hours x 4 = 48 hours for 1 painter to paint 3 rooms.
b) 1 painter to paint 1 room:
Using the same work rate, we can conclude that it will take 4 times less time for 1 painter to complete 1 room. Therefore, it will take 12 hours / 4 = 3 hours for 1 painter to paint 1 room.
c) 4 painters to paint 1 room:
Since 4 painters can complete the work in 12 hours, we can assume that the time required to paint 1 room will remain the same, regardless of the number of painters. Therefore, it will still take 12 hours for 4 painters to paint 1 room.
d) 2 painters to paint 6 rooms:
Using the same work rate, we can calculate the time required for 2 painters to paint 6 rooms. Since 1/4 rooms can be painted by the 4 painters in 1 hour, 2 painters can paint (1/4) x 2 = 1/2 room in 1 hour. Therefore, it will take 6 rooms / (1/2 room per hour) = 12 hours for 2 painters to paint 6 rooms.
4 painters paint 1 room in 12/3 = 4 hours
1 painter paints 1 room in 4/4 = 1 hour
Now you can answer the questions.