At his regular hourly rate, Don had estimated the labor cost of a repair job as $336 and he was paid that amount.

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At his regular hourly rate, Don had estimated the labor cost of a repair job as $336 and he was paid that amount. However, the job took 4 hours longer that he had estimated and, consequently, he earned $2 per hour less than his regular hourly rate. What was the time Don had estimated for the job, in hours?

A. 28
B. 24
C. 16
D. 14
E. 12

OA B

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AAPL wrote:
Thu Nov 25, 2021 8:14 am
Official Guide

At his regular hourly rate, Don had estimated the labor cost of a repair job as $336 and he was paid that amount. However, the job took 4 hours longer that he had estimated and, consequently, he earned $2 per hour less than his regular hourly rate. What was the time Don had estimated for the job, in hours?

A. 28
B. 24
C. 16
D. 14
E. 12

OA B
Here's an algebraic solution:

Let h = # of hours that Don ESTIMATED for the job.
So, h + 4 = ACTUAL # of hours it took Don to complete the job.

So, IF Don, had completed the job in h hours, his RATE would have = $336/h
However, since Don completed the job in h+4 hours, his RATE was actually = $336/(h + 4)

...consequently, he earned 2$ per hour less than his regular hourly rate.
In other words, (John's estimated rate) - 2 = (John's actual rate)
So, $336/h - 2 = $336/(h + 4)

ASIDE: since the above equation is a bit of a pain to solve, you might consider plugging in the answer choices to see which one works.

Okay, let's solve this: $336/h - 2 = $336/(h + 4)
To eliminate the fractions, multiply both sides by (h)(h+4) to get: 336(h+4) - 2(h)(h+4) = 336h
Expand: 336h + 1344 - 2h² - 8h = 336h
Simplify: -2h² - 8h + 1344 = 0
Multiply both sides by -1 to get: 2h² + 8h - 1344 = 0
Divide both sides by 2 to get: h² + 4h - 672 = 0
Factor (yeeesh!) to get: (h - 24)(h + 28) = 0
Solve to get: h = 24 or h = -28
Since h cannot be negative (in the real world), h must equal 24.

Answer: B
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