Working alone, it takes Julia 16 hours to clean an attic. Lea can clean the same attic in 15 hours. If they worked together how long would it take them?
T = T1*T2/(T1+T2) = 16*15/(16+15) =
To find out how long it would take Julia and Lea to clean the attic together, we can use the concept of work rate.
First, let's determine their individual work rates. Julia can clean the attic in 16 hours, so her work rate is 1/16 of the attic per hour. Similarly, Lea's work rate is 1/15 of the attic per hour as she can clean it in 15 hours.
When they work together, their work rates are combined, so we can add the rates. Therefore, their combined work rate is:
1/16 + 1/15 = (15 + 16) / (15 * 16) = 31/240.
This means that together, Julia and Lea can clean 31/240 of the attic per hour.
To find out how long it would take them to clean the entire attic, we need to calculate the reciprocal of their combined work rate. So, the time it would take them together is:
1 / (31/240) = 240/31 ≈ 7.74 hours.
Therefore, working together, it would take Julia and Lea approximately 7.74 hours to clean the attic.