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.
I got confuse with the rates. Please help.
Albert and Bob are painting rooms at constant,
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We can PLUG IN THE ANSWERS, which represent the time it takes Albert to paint 3n rooms.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
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.
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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: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.
(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
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