Sara can complete a painting in 6 hours, and Alex can complete the same painting in 4 hours. How long will it take them if they work together on the same painting?
Answer (2)
Sara and Alex can complete the painting together in approximately 2.4 hours, which is equivalent to 2 hours and 24 minutes. This is calculated by adding their individual rates of work and taking the reciprocal of the combined rate. Their combined effort results in a faster completion time than if they worked separately.
;
To find out how long it will take for Sara and Alex to complete the painting together, we can use the concept of work rates.
First, we need to determine the rate at which each person works:
Sara's work rate: Sara can complete the painting in 6 hours. Therefore, her work rate is 6 1 of the painting per hour.
Alex's work rate: Alex can complete the painting in 4 hours. Hence, his work rate is 4 1 of the painting per hour.
To find their combined work rate, we add their individual work rates together:
Combined work rate = 6 1 + 4 1
To add these fractions, we need a common denominator. The least common denominator of 6 and 4 is 12.
Convert each fraction to have a denominator of 12:
6 1 = 12 2 4 1 = 12 3
Add these two fractions:
12 2 + 12 3 = 12 5
The combined work rate of Sara and Alex is 12 5 of the painting per hour.
To find how long it will take them working together to complete 1 entire painting, we use the formula:
Time = Combined work rate Total work required
Since they need to complete 1 painting:
Time = 12 5 1 = 5 12
So, it will take them 5 12 hours to complete the painting together.
This can also be expressed as 2.4 hours, or 2 hours and 24 minutes.
