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?

Answer 1

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.

Answer 2

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.