SOLUTION: John is being paid $864 to do a landscape job. It took him 6 hours less than he expected, so he earned $2 per hour more than he originally calculated. How long had he anticipated

Question 767200: John is being paid $864 to do a landscape job. It took him 6 hours less than he expected, so he earned $2 per hour more than he originally calculated. How long had he anticipated it would take to do the landscaping?
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Let h = number of hours originally costed
Let r = the rate at which the h hours were costed.
Then we have
(1) r*h = 864 or
(2) h = 864/r
When he finished he was paid $864 as he charged them, but he took 6 hours less which in effect increased the hourly rate r. In the end his pay was
(3) (r+2)*(h-6) = 864
Equating (1) and (3) we get
(4)(r+2)*(h-6) = r*h or after FOILing gives us
(5) r*h - 6r + 2h - 12 = r*h or
(6) 2h = 12 + 6r or
(7) h = 6 +3r
Now equate (7) and (2) to get
(8) 3r + 6 = 864/r or after multiplying by r we get
(9) 3r^2 + 6r - 864 = 0 or after dividing by 3 we get
(10) r^2 + 2r - 288 = 0 which factors into
(11) (r + 18)*(r - 16) = 0
Taking the positive root gives us
(12) r = 16
Use (12) in (2) gives us
(13) h = 54
Let's check this with (1)
Is (16*54 = 864)?
Is (864 = 864)? Yes
Then after the job was finished he spent 54-6 or 48 hours on the job. He said that was, in effect, his original rate plus $2. Let's check this with (3).
Is ((16+2)*(54-6) = 864)?
Is (18*48 = 864)?
Is( 864 = 864)? Yes
Answer: He originally anticipated that it would take 54 hours to do the landscaping job.
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