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Luba_88 [7]
3 years ago
8

Peter takes16 minutes longer to mow the lawn by himself than Charles . Together they can mow the lawn in 18 minutes. How long wi

ll it take Charles to do it alone?
Mathematics
1 answer:
lapo4ka [179]3 years ago
7 0

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.

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