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

28
24
16
14
12

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

Cheers,
Brent

Hi All,

We’re told that Don was paid $336 for an hourly-rate for a job that he estimated would take a certainly number of hours. However, the job took 4 hours LONGER than estimated, which means he was actually paid $2/hour LESS than his normal hourly-rate for the job. We’re asked for the original number of hours that Don estimated the job would take. This question can be approached in a couple of different ways, including by TESTing THE ANSWERS.

Since the extra 4 hours spent working only decreased his normal hourly-rate by $2/hour for the job, we should start by TESTing one of the larger numbers (since the smaller the ratio of 4 hours to the original estimated time, the less impact that 4 hours would have on the average). Let’s TEST Answer B…

Answer B: 24 hours.

IF… the original estimate was 24 hours to complete the job, then Don’s hourly pay would have been $336/24 = 14 dollars/hour.

The extra 4 hours would increase the total time to 24+4 = 28 hours. In this situation, Don’s hourly pay would have been $336/28 = 12 dollars/hour. This is an exact MATCH for what we were told, so this MUST be the answer.

Final Answer: B

GMAT Assassins aren’t born, they’re made,
Rich