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?
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 ☺☺☺☺
