Question

It takes a small sprinkler 16 minutes longer to soak a lawn than it takes a larger sprinkler. working together, the sprinklers can soak the lawn in 6 minutes. how long would it take each sprinkler, working alone, to soak the lawn?

Answer 1

Let n be the large sprinkler, and n+16 be the smaller one. Then:
1/n+ 1/n+16=1/6
6/n+ 6/n+16=1
6(n+16)+6n=n²+16n
96+12n=n²+16n
n²+4n-96=0
(n+12)(n-8)=0
n=8 or -12
Using the positive value, we get the large sprinkler soaking the lawn in 8 minutes, and the smaller sprinkler taking 24 minutes
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