SOLUTION: Hi If 2 teams work together they can finish a job in 8 days. The rate of work of the first team is 5/8 of the rate of the second team. How many days each team needs to compl

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Question 1151742: Hi
If 2 teams work together they can finish a job in 8 days. The rate of work of the first team is 5/8 of the rate of the second team. How many days each team needs to complete this job working alone.
Thanks
Found 3 solutions by josmiceli, ikleyn, greenestamps:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = the rate of the faster team
= the rate of the slower team
= the rate of the teams working together
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and



The slower team does the job in 20.8 days
The faster team does the job in 13 days
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Get a 2nd opinion if needed
Answer by ikleyn(52765)   (Show Source): You can put this solution on YOUR website!
.

Let x be the rate of work of the second team.


Then the rate of work of the first team is  ,  according to the condition.


The rate of work of BOTH teams working together is then   = .


From the condition,


     = .


Hence,  x = .


It means that the second team can complete the job in  13 days.


Then the first team's rate of work is    of the job per day.


It means that the first team will complete the job in    =  =  =   days.


ANSWER.  The second team will complete the job in 13 days.

         The first team will complete the job in    days.

Solved.


Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


Since the rate of the first team is 5/8 the rate of the second team, when working together the first team does 5/13 of the work and the second team does 8/13 of the work.

So when the two teams working together do the job in 8 days, the first team does 5/13 of the work in those 8 days. So the number of days they would take to do the whole job alone is



Similarly, since the second team does 8/13 of the work in those 8 days, the number of days they would take to do the job alone is



ANSWERS:
The first team would take 20.8 days to do the job alone.
The second team would take 13 days to do the job alone.
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