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21 Mar 2018, 23:05
00:00

Difficulty:

45% (medium)

Question Stats:

72% (02:51) correct 28% (03:20) wrong based on 43 sessions

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A painter was paid $800 as labor cost for painting the exterior of the front of a house. This amount was the painter’s estimated labor cost based on a regular rate of R, in dollars per hour, for an estimated time T, in hours. However, the actual time it took for the painter to do the job was 4 hours longer than the estimated time, thereby reducing the hourly rate for the job by$10 per hour. What is R, the painter’s regular rate, in dollars per hour?

(A) 20
(B) 30
(C) 40
(D) 50
(E) 60

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22 Mar 2018, 01:21
Bunuel wrote:
A painter was paid $800 as labor cost for painting the exterior of the front of a house. This amount was the painter’s estimated labor cost based on a regular rate of R, in dollars per hour, for an estimated time T, in hours. However, the actual time it took for the painter to do the job was 4 hours longer than the estimated time, thereby reducing the hourly rate for the job by$10 per hour. What is R, the painter’s regular rate, in dollars per hour?

(A) 20
(B) 30
(C) 40
(D) 50
(E) 60

This is an Alternative approach and is especially useful if long word problems tend to confuse you.

Starting with the median - C.
If the regular rate is 40 then the regular time is 800/40 = 20. In this case the new rate was 40-10=30 and the new time was 800/30 = 80/3. Since 20 + 4 does not equal 80/3, this answer is incorrect.
Let's try the next largest answer, (D).
If the regular rate is 50 then the regular time is 800/50 = 16. In this case the new rate was 50-10=40 and the new time was 800/40 = 20. Since 16 + 4 = 20 then all our calculations work out and our answer is (D).

Note that you don't actually need to write down any equations with variables to use this approach.
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Re: A painter was paid $800 as labor cost for painting the exterior of the [#permalink] ### Show Tags 22 Mar 2018, 17:09 Bunuel wrote: A painter was paid$800 as labor cost for painting the exterior of the front of a house. This amount was the painter’s estimated labor cost based on a regular rate of R, in dollars per hour, for an estimated time T, in hours. However, the actual time it took for the painter to do the job was 4 hours longer than the estimated time, thereby reducing the hourly rate for the job by $10 per hour. What is R, the painter’s regular rate, in dollars per hour? (A) 20 (B) 30 (C) 40 (D) 50 (E) 60 Answer choices For each answer's rate and decreased rate, find time taken. The difference in hours should be 4. Rate * Time = Pay, P Thus, Time, $$T = \frac{P}{R}$$ Start with C)$40 per hour (estimated). $30 per hour (actual) Time at$40: $$\frac{800}{40per.hr}= 20$$ hours
Time at $30: $$\frac{800}{30per.hr}=\frac{80}{3}= 26.xx$$ hours 800/30 is not an integer. I calculated to find out whether$40 per hour = too high or too low

6.xx extra hours. Too great. Needs to decrease.

R and T are inversely proportional
(one increases, the other decreases)
T needs to come down. R must go up.
$40 per hour is too low Try D)$50 per hour (estimated). $40 per hour (actual) Time at$50: $$\frac{800}{50} = 16$$ hours
Time at $40, from above = $$20$$ hours Difference? 4 hours. That's correct. Answer D Algebra (Hourly pay rate) * (# hours worked) = Total pay in dollars Same basis as $$RT = W$$ $$RT = W$$, so $$T = \frac{W}{R}$$ W = 800 Estimated rate = $$r$$ Actual rate = $$r-10$$ Estimated time = $$\frac{800}{r}$$ Actual time = $$\frac{800}{r-10}$$ To find rate, $$r$$, use time, which is defined in terms of $$r$$ (Actual time) - (estimated time) = $$4$$ hours $$\frac{800}{r-10} - \frac{800}{r} = 4$$ $$\frac{800r - 800(r-10)}{r(r-10)} = 4$$ $$800r - 800r + 8000 = 4* r(r-10)$$ $$8000 = 4 * r(r-10)$$ $$2000 = r^2 - 10r$$ $$r^2 - 10r - 2000 = 0$$ $$(r - 50)(r + 40) = 0$$ $$r = 50$$ Answer D _________________ SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here. Instructions for living a life. Pay attention. Be astonished. Tell about it. -- Mary Oliver Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2815 Re: A painter was paid$800 as labor cost for painting the exterior of the  [#permalink]

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23 Mar 2018, 12:41
Bunuel wrote:
A painter was paid $800 as labor cost for painting the exterior of the front of a house. This amount was the painter’s estimated labor cost based on a regular rate of R, in dollars per hour, for an estimated time T, in hours. However, the actual time it took for the painter to do the job was 4 hours longer than the estimated time, thereby reducing the hourly rate for the job by$10 per hour. What is R, the painter’s regular rate, in dollars per hour?

(A) 20
(B) 30
(C) 40
(D) 50
(E) 60

We can create the equation:

RT = 800

T = 800/R

and

(T + 4)(R - 10) = 800

RT + 4R - 10T - 40 = 800

RT + 4R - 10T = 840

Substituting, we have:

R(800/R) + 4R - 10(800/R) = 840

800 + 4R - 8000/R = 840

4R - 8000/R = 40

Multiplying by R, we have:

4R^2 - 8000 = 40R

4R^2 - 40R - 8000 = 0

Dividing by 4, we have:

R^2 - 10R - 2000 = 0

(R - 50)(R + 40) = 0

R = 50 or R = -40

Since R can’t be negative, R = 50.

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26 Mar 2018, 11:16
Wasted my time trying to go for an algebraic solution but such questions could best be solved using options.
We know that - R*T=800.
Let C be the correct answer.
Then, R=40; T=20.

Now, T is increased by 4 hours and R is reduced by $10. R(new) = 30; T(new) = 24. -> RT(New) = 720. So we know that R cannot be 20 and 30 either because the decrease in number is by 10 while the increase is by 4 only. Thus, the product will get smaller. Therefore, for easier calculations, let R=50, then T=16. When R is reduced by$10 and T is increased by 4 hours, then R=40 and T=20.

Thus, both remain the same.

So the correct answer is 50.
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