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!

The correct answer is E.

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.

Answer: E