Albert and Bob are painting rooms at constant, but different

Sourabh2012 · **Posted:** Sun Feb 05, 2012 7:24 pm


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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

Please help, totally stumped. Looking for some simpler and quick approach.

[Reveal] Spoiler: OA

E

kys123 · **Posted:** Sun Feb 05, 2012 10:51 pm

rate of bob to paint n rooms is n/T(bob)
rate of Albert to paint n rooms is n/T(albert).
albert paints the room 1 hour slower than bob, so T (albert) = T(bob) -1
Together they paint the 3n/5 rooms in 4/3 hours. Rate is equal to work over time

Therefore
n/x + n/x-1 = (3n/5)/(4/3) =
n/x + n/x-1 = 9n/20. Fastest way for me is to think how would make the denominator 20. 4*5 = 20 and it fits x and x-1 or you can solve the quadratic
4n/20 + 5n/20 = 9n/20. Therefore you know it takes Albert 5 hours to paint n room, since Albert's rate is n/5.
5*3 = 3n
15 = 3n.

Answer is E

VeritasPrepKarishma · **Posted:** Mon Feb 06, 2012 2:31 am

sourabhsoni 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

Please help, totally stumped. Looking for some simpler and quick approach.

First of all, I don't like unnecessary variables. The data given is in terms of n rooms but the answer is independent of n. This means, no matter what value I put for n, the answer would be the same. So I will just put n = 1 and proceed.

Albert takes an hour longer than Bob to paint one room.
Time taken by Albert to paint 1 room = A hrs, Time taken by Bob = A-1 hrs

"they can paint a total of 3/5 rooms in 4/3 hours"
W = R*T
3/5 = R*(4/3)
R = 9/20 which is the combined rate of the two.

We obtained this by adding their rates together: 9/20 = 1/A + 1/(A-1)
Over here, please remember that numbers fall in place in GMAT questions. You should be able to figure that since the denominator is 20, A = 5 gives 5*4 in the denominator so it should work. Check before proceeding though.

So Albert paints a room in 5 hrs. For 3 rooms, he takes 3*5 = 15 hrs.

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