Question 567792
A student did a word-processing job for $42.
 It took him 8 hours longer than he expected, and therefore he earned $4 per hour less than he anticipated.
 How long did he expect that it would take to do the job?
:
Let t = time he expected to do the job
then
{{{42/t}}} = his expected hourly pay
:
Let (t+8) = his actual time to do the job
then
{{{42/((t+8))}}} = his actual hourly pay
:
The equation
expect hrly pay - actual hrly pay = $4
{{{42/t}}} - {{{42/((t+8))}}} = 4
multiply by t(t+8), resulting in:
42(t+8) - 42t = 4t(t+8)
:
42t + 336 - 42t = 4t^2 + 32t
Arrange as a quadratic equation
4t^2 + 32t - 336 = 0
Simplify, divide by 4
t^2 + 8t - 84 = 0
Factors to
(t+14)(t-6) = 0
the positive solution
t = 6 hrs was his anticipated time for the job
:
:
Check this by finding the actual hourly pay
42/6 = $7 an hr
42/14= $3 an hr
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differ: $4