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amina.shaikh309
- Senior | Next Rank: 100 Posts
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- Joined: Sat Apr 23, 2016 9:06 pm
Here's an algebraic solution: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
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
