SOLUTION: If two construction teams work together, they can finish a road in 15 days. The rate of work of the first team is 4/5 of the rate of the second team. How many days each team ne

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Question 1154864: If two construction teams work together, they can finish a road in 15 days. The rate of work of the first team is 4/5 of the rate of the second team.
How many days each team needs to complete this job alone?
Found 2 solutions by mananth, VFBundy:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

If two construction teams work together they can finish a road in 15 days.the rate of work of the first team is 4/5 of the rate of the second team.
How many days each team needs to complete this job alone.
Let one team take x hours to do the job
This team does 1/x of the job in 1 hour alone
They take (4/5)x hours to do the job
This team does (5/4x) of the job in 1 hour alone
Both together do the job in 15 days
Together the complete 1/15 of the job in1 hour
+1%2Fx+%2B%285%2F4x%29+=+1%2F15
%28%289%2F4x%29=1%2F15+
4x = 135
x =135/4
x =33.75
First team 33.75 days
II team
(4/5)*33.75 =27 days

Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
Rate of work of first team = %284%2F5%29%281%2Fx%29 = 4%2F5x
Rate of work of second team = 1%2Fx

Rate of work working together = %284%2F5x%29+%2B+%281%2Fx%29 = 1%2F15 --> %284%2F5x%29+%2B+%285%2F5x%29 = 1%2F15 --> %289%2F5x%29 = 1%2F15 --> 5x+=+135 --> x+=++27

Plug in x = 27:

Rate of work of first team = %284%2F5%29%281%2Fx%29 = 4%2F5x = 4%2F135
Rate of work of second team = 1%2Fx = 1%2F27

Since the first team completes 4/135 of the job per day, this means it will take them 135/4 days...or 33.75 days...to complete the job working alone.

Since the second team completes 1/27 of the job per day, this means it will take them 27 days to complete the job working alone.