Gary Glaze requires 25 hours to put a new roof on a house. His apprentice, Anna Gandy, can reroof the house by herself in 32 hours. After working alone on a roof for 20 hours, Gary leaves for another job. Anna takes over and completes the job. How long does it take Anna to complete the job?
Gray's rate = 1/25
Anna' rate = 1/32
Job done by Gray = 20(1/25) = 4/5
leaving 1/5 of the job left to be done by Anna
time for Anna to complete
= (1/5) / (1/32)
= 6.4
It will take her 6.4 days to finish the roof.
Gary completes 20/25 or 4/5 of the roof.
5/5-4/5 = 1/5 = 0.2 of roof remains.
1/32 = 0.2/T.
T = 6.4 Hours.
Let's calculate the rate at which each worker completes the job:
Gary's rate = 1 roof / 25 hours
Anna's rate = 1 roof / 32 hours
Since Anna completes the job alone, we can use her rate to calculate the time it takes for her to complete the job after Gary leaves.
Anna's rate = 1 roof / x hours
To find x, we can use the formula:
1/32 + 1/x = 1/25
Multiplying through by 32 * 25 * x, we get:
25x + 32 * 25 = 32x
Simplifying, we have:
800 = 7x
Dividing both sides by 7, we find:
x = 114.29
Therefore, it takes Anna approximately 114.29 hours to complete the job on her own.
To find out how long it takes Anna to complete the job, we need to calculate the work rate of both Gary and Anna.
Gary's work rate: 1 roof / 25 hours = 1/25 roof per hour.
Anna's work rate: 1 roof / 32 hours = 1/32 roof per hour.
Since we are given that Gary worked alone for 20 hours, we can calculate the work done by Gary in that time frame.
Work done by Gary = Gary's work rate * time = (1/25) * 20 = 20/25 = 4/5 roof.
Now, to determine how long it takes Anna to complete the remaining work, we subtract the work done by Gary from the total work needed.
Remaining work = 1 roof - 4/5 roof = 1/5 roof.
Now we can calculate the time it takes Anna to complete the remaining work.
Time taken by Anna = Remaining work / Anna's work rate = (1/5) / (1/32) = (1/5) * (32/1) = 32/5 = 6.4 hours.
Therefore, it takes Anna 6.4 hours to complete the job.