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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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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3142

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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

R*T = 800
(R-10) * (T+4) = 800
if R = 50 then T = 16
Then R becomes 40 and T becomes 20

Hence D
examPAL Representative P
Joined: 07 Dec 2017
Posts: 1155

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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

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.

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

$$\frac{800}{r-10} - \frac{800}{r} = 4$$

$$\frac{800r - 800(r-10)}{r(r-10)} = 4$$

$$800r - 800r + 8000 = 4* r(r-10)$$

$$8000 = 4 * r(r-10)$$

$$2000 = r^2 - 10r$$

$$r^2 - 10r - 2000 = 0$$

$$(r - 50)(r + 40) = 0$$

$$r = 50$$

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Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2812

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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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"Success is a lousy teacher. It seduces smart people to think they can't lose" - Bill Gates. Re: A painter was paid $800 as labor cost for painting the exterior of the [#permalink] 26 Mar 2018, 11:16 Display posts from previous: Sort by # A painter was paid$800 as labor cost for painting the exterior of the  