Gray Glaze requires 15 hours to put a new roof on a house. His apprentice, Anna Gandy, can record the house by herself in 20 hours. After working alone on a roof for 6 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 = 1/15
Anna' rate = 1/20
Job done by Gray = 6(1/15) = 2/5
leaving 3/5 of the job left to be done by Anna
time for Anna to complete
= (3/5) / (1/20)
= 12
It will take her 12 days to finish the roof
To find out how long it takes Anna to complete the job, we need to first determine how much work Gary and Anna do together in the 6 hours Gary is working.
Gary's rate of work is 1/15 of the house per hour, which means he can complete 1/15th of the roof in one hour.
In 6 hours, Gary will complete 6 * (1/15) = 6/15 = 2/5 of the roof.
Now, we can calculate how much work is left for Anna to complete on her own. Since Anna can complete the whole roof in 20 hours, her rate of work is 1/20 of the roof per hour.
The work left for Anna to complete is 1 - (2/5) = 3/5 of the roof.
Now, we can find out how long it takes Anna to complete the remaining work on her own. Since her rate of work is 1/20 of the roof per hour, she will take (3/5) / (1/20) = (3/5) * (20/1) = 60/5 = 12 hours to complete the job.
Therefore, it takes Anna 12 hours to complete the job.