SOLUTION: There is a project. Company A needs 24 days to finish. Company B needs 30 days to finish. If A and B collaborate for 8 days, then it takes 6 more days for company C to finish the r

Question 1163729: There is a project. Company A needs 24 days to finish. Company B needs 30 days to finish. If A and B collaborate for 8 days, then it takes 6 more days for company C to finish the rest. How long does it take for company C alone to finish the project?
Found 4 solutions by ikleyn, solver91311, ankor@dixie-net.com, MathTherapy:
Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
.
There is a project. Company A needs 24 days to finish. Company B needs 30 days to finish. If A and B collaborate for 8 days,
then it takes 6 more days for company C to finish the rest. How long does it take for company C alone to finish the project?
~~~~~~~~~~~~~~~

Working 8 days, company A will make = of the job; company B will make = of the job. So, in 8 days the companies A and B will complete + = = = of the job. The rest is 1 - = of the job; hence, the rate of company C is = = . It means that company C can complete the whole project in 15 days working alone. ANSWER

Solved.

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All you need is to know the notion/conception of the "rate of work" and to have skills manipulating fractions.

You even do not need write and solve equations.

From this point of view, it is a "Pre-algebra" level problem.

Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

A takes 24 days for the whole job, so A can do of the job in one day. Likewise B can do of the job in one day. Working together they can do of the job in 1 day. So in 8 days, they accomplish of the job, leaving C to finish of the job in 6 days. If C takes 6 days to accomplish of the job, then C can do of the total job in one day, so C can accomplish the whole job in days.

John

My calculator said it, I believe it, that settles it

Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
There is a project.
Company A needs 24 days to finish.
Company B needs 30 days to finish.
If A and B collaborate for 8 days, then it takes 6 more days for company C to finish the rest.
How long does it take for company C alone to finish the project?
:
let the completed job = 1
+ + = 1
+ + = 1
+ = 1
multiply by 15c
9c + 6(15) = 15c
90 = 15c - 9c
6c = 90
c = 15 days for C to do the job alone
Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!

There is a project. Company A needs 24 days to finish. Company B needs 30 days to finish. If A and B collaborate for 8 days, then it takes 6 more days for company C to finish the rest. How long does it take for company C alone to finish the project?

Let time C takes to complete job, alone, be C
Since it's 1 ENTIRE job, we then get:
5C + 4C + 90 = 15C ------ Multiplying by LCD, 15C
9C + 90 = 15C
90 = 15C - 9C
90 = 6C
Time C takes to complete the job, by itself, or
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