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

Algebra ->  Rate-of-work-word-problems -> 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       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of soaking to get their
rate of soaking together
Let +t+ = the time in minutes for the larger sprinkler to soak lawn
+t+%2B+16+ is the time in minutes for the smaller sprinkler to soak lawn
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Rate for larger sprinkler = ( 1 lawn ) / ( t min )\
Rate for smaller sprinkler = ( 1 lawn ) / ( t + 16 min )
Rate working together = ( 1 lawn ) / ( 6 min )
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+1%2Ft+%2B+1%2F%28+t+%2B+16+%29+=+1%2F6+
Multiply each sides by +6t%2A%28+t+%2B+16+%29+
+6%2A%28+t+%2B+16+%29+%2B+6t+=+t%2A%28+t+%2B+16+%29+
+6t+%2B+96+%2B+6t+=+t%5E2+%2B+16t+
+t%5E2+%2B+4t+=+96+
Complete the square
+t%5E2+%2B+4t+%2B+%284%2F2%29%5E2+=+96+%2B+%284%2F2%29%5E2+
+t%5E2+%2B+4t+%2B+4+=+96+%2B+4+
+%28+t+%2B+2+%29%5E2+=+10%5E2+
Take the square root of both sides
+t+%2B+2+=+10+ ( ignore the negative square root of 100 )
+t+=+8+
and
+t+%2B+16+=+24+
The smaller sprinkler takes 24 min
The larger one takes 8 min
check:
+1%2Ft+%2B+1%2F%28+t+%2B+16+%29+=+1%2F6+
+1%2F8+%2B+1%2F24+=+1%2F6+
+3%2F24+%2B+1%2F24+=+4%2F24+
+4%2F24+=+4%2F24+
OK