SOLUTION: Kermit has agreed to paint Miss Piggy's house for $640.00. Unfortunately, it took Kermit 20 hours longer to paint the house than he had planned and he earned $1.60 per hour less th

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Question 1060291: Kermit has agreed to paint Miss Piggy's house for $640.00. Unfortunately, it took Kermit 20 hours longer to paint the house than he had planned and he earned $1.60 per hour less than he had previously calculated. How much was Kermit's anticipated hourly wage to paint Miss Piggy's house?
Answer by ikleyn(52776) About Me  (Show Source):
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Kermit has agreed to paint Miss Piggy's house for $640.00. Unfortunately, it took Kermit 20 hours longer to paint the house
than he had planned and he earned $1.60 per hour less than he had previously calculated.
How much was Kermit's anticipated hourly wage to paint Miss Piggy's house?
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Let "a be Kermit's anticipated hourly wage, in dollars.
Then his real hourly wage was (a-1.6) dollars.

So, Kermit originally planned to complete the job in 640%2Fa hours.
But in reality he spent 640%2F%28a-1.6%29 hours.

The difference is 20 hours. It gives you an equation

640%2F%28a-1.6%29 - 640%2Fa = 20.

To solve it, multiply both sides by a*(a-1.6). You will ge

640a - 640(a-1.6) = 20a(a-1.6).

20a%5E2+-32a+-+1024 = 0,

5a%5E2+-+8a+-+256 = 0,

a%7B1%2C2%5D = . . . %288+%2B-+72%29%2F10.

The positive solution is a = 8.

Answer.  Kermit's anticipated hourly wage of $8.

Check.   640%2F8 = 80 hours.  640%2F%288-1.6%29 = 640%2F6.4 = 100.  100 - 80 = 20.  Correct !

Solved.