A man did a job for $168. It took him 2 hours longer than he expected, and therefore he earned $2 per hour less than he anticipated. How long did he expect that it would take to do the job?
A) 17 hours
B) 9 hours
C) 14 hours
D) 12 hours
E) 7 hours

Question

Quizplus · Accepted Answer

Let's call the expected number of hours "x". Then he actually worked for "x+2" hours, and earned "$2 less per hour" than he expected, which means he earned $(2 less per hour) = $(2-x) per hour. The total amount he earned is given as $168, so we can set up an equation:

(x+2)(2-x) = 168

Expanding this out and simplifying gives:

-x^2 + 2x + 4x - 4 = 168
-x^2 + 6x - 172 = 0

We can solve for x using the quadratic formula:

x = (-6 ± sqrt(6^2 - 4(-1)(-172))) / (2(-1))
x = (-6 ± sqrt(1508)) / 2
x = (-6 ± 38.84) / 2

We're only interested in the positive solution, so:

x = (-6 + 38.84) / 2
x = 16.92

Therefore, he expected it to take about 16.92 hours to do the job, which we can round to 17 hours. The closest answer choice is (A) 17 hours, so that is the best choice.

A Man Did a Job for $168