SOLUTION: It takes a small sprinkler 12 min longer to soak a lawn than it takes a large sprinkler. Working together, the sprinklers can soak the lawn in 8 min. How long would it take each sp
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Question 861017: It takes a small sprinkler 12 min longer to soak a lawn than it takes a large sprinkler. Working together, the sprinklers can soak the lawn in 8 min. How long would it take each sprinkler, working alone, to soak the lawn?
small sprinkler
______
min
large sprinkler ______ min.
You can put this solution on YOUR website! It takes a small sprinkler 12 min longer to soak a lawn than it takes a large sprinkler.
Working together, the sprinklers can soak the lawn in 8 min.
How long would it take each sprinkler, working alone, to soak the lawn?
:
let t = time required by the larger sprinkler
then
(t+12) = time required by the small
:
the completed job = 1 (a soaked lawn)
:
Each will do a fraction of the job, the two fractions add up to 1 + = 1
multiply by t(t+12) to clear the denominators, results:
8(t+12) + 8t = t(t+12)
8t + 96 + 8t = t^2 + 12t
combine to form a quadratic on the right
0 = t^2 + 12t - 16t - 96
t^@ - 4t - 96 = 0
Factors to
(t-12)(t+8) = 0
positive solution
t = 12 min for the larger sprinkler
and
12 + 12 = 24 min for the small one
