Answer:
about 29.7 minutes
Step-by-step explanation:
If it take c minutes for Charles to mow the lawn by himself, it takes c+16 minutes for Peter. The two of them working together can mow in one minute this fraction of the entire lawn:
1/c + 1/(c+16) = 1/18
Multiplying by 18c(c+16), we get ...
18(c +16) + 18(c) = c(c+16)/18
36c +288 = c^2 +16c
c^2 -20c = 288 . . . . . subtract 36c
c^2 -20c +100 = 388 . . . . . add (20/2)^2 = 100 to complete the square
(c -10)^2 = 388
c = 10 +√388 ≈ 29.6977 . . . . . take the positive square root
It takes Charles about 29.7 minutes to mow the lawn by himself.
