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) About Me  (Show Source):
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Let +r+ = the rate of the faster team
+%285%2F8%29%2Ar+ = the rate of the slower team
+1%2F8+ = the rate of the teams working together
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+r+%2B+%28+5%2F8+%29%2Ar+=+1%2F8+
+%28+13%2F8+%29%2Ar+=+1%2F8+
+13r+=+1+
+r+=+1%2F13+
and
+%28+5%2F8+%29%2Ar+=+%28+5%2F8+%29%2A%28+1%2F13+%29+
+%28+5%2F8+%29%2Ar+=+5%2F104+
+%28+5%2F8%29%2Ar+=+1%2F20.8+
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(52762) About Me  (Show Source):
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.

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


Then the rate of work of the first team is  %285%2F8%29%2Ax,  according to the condition.


The rate of work of BOTH teams working together is then  x+%2B+%285%2F8%29%2Ax = %2813%2F8%29%2Ax.


From the condition,


    %2813%2F8%29%2Ax = 1%2F8.


Hence,  x = 1%2F13.


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


Then the first team's rate of work is  %285%2F8%29%2A%281%2F13%29  of the job per day.


It means that the first team will complete the job in   %281%2F%28%285%2F8%29%29%29%2A%281%2F%28%281%2F13%29%29%29 = %288%2A13%29%2F5 = 104%2F5 = 204%2F5  days.


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

         The first team will complete the job in  204%2F5  days.

Solved.


Answer by greenestamps(13196) About Me  (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

8%2F%285%2F13%29+=+8%2A%2813%2F5%29+=+104%2F5+=+20.8

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

8%2F%288%2F13%29+=+8%2A%2813%2F8%29+=+13

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.