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## Albert and Bob are painting rooms at constant,

This topic has 2 expert replies and 0 member replies

### Top Member

Vincen Master | Next Rank: 500 Posts
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#### Albert and Bob are painting rooms at constant,

Thu Sep 14, 2017 2:00 pm
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
Albert and Bob are painting rooms at constant, but different rates. Albert takes 1 hour longer than Bob to paint n rooms. Working side by side, they can paint a total of 3n/5 rooms in 4/3 hours. How many hours would it take Albert to paint 3n rooms by himself?

A. 7
B. 9
C. 11
D.13
E. 15

The OA is E.

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### GMAT/MBA Expert

GMATGuruNY GMAT Instructor
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Thu Sep 14, 2017 7:13 pm
Vincen wrote:
Albert and Bob are painting rooms at constant, but different rates. Albert takes 1 hour longer than Bob to paint n rooms. Working side by side, they can paint a total of 3n/5 rooms in 4/3 hours. How many hours would it take Albert to paint 3n rooms by himself?

A. 7
B. 9
C. 11
D.13
E. 15
We can PLUG IN THE ANSWERS, which represent the time it takes Albert to paint 3n rooms.
When the correct answer is plugged in, the time for Albert and Bob to paint 3n/5 rooms will be 4/3 hours.

The answer choices indicate that the time for Albert to paint 3n rooms must be one of the following:
7, 9, 11, 13, 15.
Thus, the time for Albert to paint n rooms must be 1/3 of the correct answer choice.
Implication:
The correct answer is likely to be divisible by 3.

E: 15
Since Albert takes 15 hours to paint 3n rooms, the time for Albert to paint n rooms = (1/3)(15) = 5 hours.
Since Albert takes 1 hour longer than Bob to paint n rooms, the time for Bob to paint n rooms = 5-1 = 4 hours.
Let n=20.
Rate for Albert = w/t = 20/5 = 4 rooms per hour.
Rate for Bob = w/t = 20/4 = 5 rooms per hour.
Combined rate for Albert and Bob = 4+5 = 9 rooms per hour.
Number of rooms to be painted = 3n/5 = (3*20)/5 = 12 rooms.
Time for Albert and Bob to paint 12 rooms = w/r = 12/9 = 4/3 hours.
Success!

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### GMAT/MBA Expert

Jeff@TargetTestPrep GMAT Instructor
Joined
09 Apr 2015
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Tue Sep 19, 2017 2:53 pm
Vincen wrote:
Albert and Bob are painting rooms at constant, but different rates. Albert takes 1 hour longer than Bob to paint n rooms. Working side by side, they can paint a total of 3n/5 rooms in 4/3 hours. How many hours would it take Albert to paint 3n rooms by himself?

A. 7
B. 9
C. 11
D.13
E. 15

The OA is E.
We can let b = the number of hours Bob takes to paint n rooms; thus, Bob’s rate = n/b and Albert’s rate = n/(b + 1). Knowing that they can complete 3n/5 rooms in 4/3 hours, we can create the following equation:

(n/b)(4/3) + [n/(b + 1)](4/3) = 3n/5

4n/3b + 4n/[3(b + 1)] = 3n/5

Multiplying the entire equation by 3b x 5 x (b + 1) = 15b(b + 1), we have:

4n[5(b + 1)] + 4n(5b) = 3n[3b(b + 1)]

Dividing by n, we have:

20(b + 1) + 20b = 9b(b + 1)

20b + 20 + 20b = 9b^2 + 9b

9b^2 - 31b - 20 = 0

(9b + 5)(b - 4) = 0

b = -5/9 or b = 4

Since b can’t be negative, b = 4. Thus, it takes Albert 4 + 1 = 5 hours to paint n rooms and 5 x 3 = 15 hours to paint 3n rooms.

_________________
Jeffrey Miller Head of GMAT Instruction

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