Question about Office Equipment & Supplies
I will try to solve it systematically so it will be easier to understand. Note: The solution involves solving a quadratic equation.
Let amount of hours estimated be x:
Expected rate: $18000/(x hours)
Time spent extra: 6 hours.
Totals hours spent: (x + 6) hours
New rate: $18000/(x+6 hours)
The new rate is less than old rate by $100, therefore we can make the above inequality equality by adding $100 to the new rate.
18000/(x+6) + 100 = 18000/x
Solve by cross multiplaction:
(18000 + 100(x+6) * x = 18000 * (x+6)
18000x + 100x(x+6) = 18000x + 108000
100x(x+6) = 108000 (cancel 18000x on both sides)
x(x+6) = 1080 (divide by 100)
x^2 + 6x - 1080 = 0
Solve the above quadratic equation by any method (completing square, factorization or quadratic formula)
x = (-b+-(b^2 - 4ac)^.5)/2a where a = 1; b = 6; c = -1080
x = 30 or -36 (hours cannot be negative so disregard this result)
Therefore x = Estimated time = 30 hours
18000/30 = $600 per hour x+6 = 36 $18000/36 = $500 or $100 per hour less than estimated
Posted on Nov 13, 2010
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Posted on Jan 02, 2017
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