SOLUTION: It takes a small sprinkler 16 minutes longer to soak a lawn than it takes a larger sprinkler. working together, the sprinklers can soak a lawn in 6 minutes. How long would it take
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Question 597625: It takes a small sprinkler 16 minutes longer to soak a lawn than it takes a larger sprinkler. working together, the sprinklers can soak a lawn in 6 minutes. How long would it take each sprinkler,working alone, to soak the lawn?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Add their rates of soaking to get their
rate of soaking together
Let = the time in minutes for the larger sprinkler to soak lawn
is the time in minutes for the smaller sprinkler to soak lawn
--------------
Rate for larger sprinkler = ( 1 lawn ) / ( t min )\
Rate for smaller sprinkler = ( 1 lawn ) / ( t + 16 min )
Rate working together = ( 1 lawn ) / ( 6 min )
--------------
Multiply each sides by
Complete the square
Take the square root of both sides
( ignore the negative square root of )
and
The smaller sprinkler takes 24 min
The larger one takes 8 min
check:
OK
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