It takes 2 hours for Jay to paint a wall and 3 hours for his brother Bong. How long will it take for the 2 of them working together?
Answer (1)
Answer:Determine each person's work rate:Jay can paint the wall in 2 hours, so his work rate is 1221 of the wall per hour.Bong can paint the wall in 3 hours, so his work rate is 1331 of the wall per hour.Add their work rates together to find the combined work rate:Combined work rate=12+13Combined work rate= 21 + 31 To add these fractions, find a common denominator. The least common denominator of 2 and 3 is 6. Convert each fraction:12=36and13=2621 = 63 and 31 = 62 Adding these gives:36+26=5663 + 62 = 65 So, their combined work rate is 5665 of the wall per hour.Calculate the time required to paint the wall together: The combined work rate tells us that together they can paint 5665 of the wall in one hour. To find the time to paint the entire wall, take the reciprocal of the combined work rate:Time=1Combined work rate=156=65 hoursTime= Combined work rate1 = 65 1 = 56 hoursThis simplifies to 1.2 hours.So, it will take Jay and Bong 1.2 hours (or 1 hour and 12 minutes) to paint the wall together.
