SOLUTION: There is a project. Company A alone needs 20 days to finish. If A works with B, then it takes 12 days. If A works for 16 days alone, B will finish the rest. How many days are neede
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Question 1163735: There is a project. Company A alone needs 20 days to finish. If A works with B, then it takes 12 days. If A works for 16 days alone, B will finish the rest. How many days are needed for B to finish it? Found 2 solutions by ankor@dixie-net.com, greenestamps:Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! There is a project. Company A alone needs 20 days to finish.
If A works with B, then it takes 12 days.
b = time for B to do the job alone
let the completed job = 1 + = 1
multiply 20b
12b + 20(12) = 20b
12b + 240 = 20b
240 = 20b - 12b
240 = 8b
b = 240/8
b = 30 days, B by itself
:
If A works for 16 days alone, B will finish the rest.
How many days are needed for B to finish it?
let d = time for B to finish the job + = 1
multiply equation by 60
3(16) + 2d = 60
2d = 60 - 48
2d = 12
d = 12/2
d = 6 days for B to finish the job
There are many ways to solve the problem using formal algebra; the other tutor showed one good way.
If a formal algebraic solution is not required, I like to encourage students to solve the problem informally with logical reasoning and mental arithmetic. The mental exercise you get by THINKING your way through the problem will be good for you.
A alone can do the whole job in 20 days. So when A and B together complete the job in 12 days, the fraction of the job that A does is 12/20 = 3/5.
That means in 12 days B does 2/5 of the job.
A working alone for 16 days will complete 16/20 = 4/5 of the job; 1/5 of the job will remain to be done.
Since B can do 2/5 of the job in 12 days, he can do 1/5 of the job in 6 days.
