SOLUTION: An experienced bricklayer can work twice as fast as an apprentice bricklayer. After they worked together on a job for 12 h, the experienced bricklayer quit. The apprentice required

Algebra ->  Signed-numbers -> SOLUTION: An experienced bricklayer can work twice as fast as an apprentice bricklayer. After they worked together on a job for 12 h, the experienced bricklayer quit. The apprentice required      Log On


   

Question 373417: An experienced bricklayer can work twice as fast as an apprentice bricklayer. After they worked together on a job for 12 h, the experienced bricklayer quit. The apprentice required 12 more hours to finish the job. How long would it take the experienced bricklayer, working alone, to do the job?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let r = the apprentices rate of working
Then 2r = the experienced bricklayer's rate of working
If I add their rates and multiply by hours worked, that
will give me the fraction of the job completed
When the experienced bricklayer quit, that fraction is
%28r+%2B+2r%29%2A12
Now the remaining fraction of the job is done in 12 hours
That fraction is r%2A12+
Now I can say
3r%2A12+=+1+-+r%2A12
36r+=+1+-+12r
48r+=+1
r+=+1%2F48
2r+=+2%2F48
2r+=+1%2F24
The experienced bricklayer takes 24 hours to do the job alone
check answer:
%28r+%2B+2r%29%2A12+=+3%2A%281%2F48%29%2A12
%283%2F48%29%2A12+=+3%2F4
r%2A12+=+12%2F48
12%2F48+=+1%2F4
Working together, they did 3/4 of the job
Then the apprentice did 1/4 of the job alone