tough knewton PS

bob takes t-1 hours to paint n rooms
Albert takes t hours
work=n
rate A = n/(t)
rate B = n/(t-1)
total rate = n(2t-1)/((t)*(t-1))
time to paint n rooms = (t)(t-1)/(2t-1)
to paint 3n/5 rooms = 3(t)(t-1)/5*(2t-1) = 4/3
9t^2 - 9t = 40t - 20
9t^2 -49t + 20 =0
t = (49 +-root(41)/18 = 5 hours
Thus 3n rooms means 15 hours.
IMO E

Hi,
Let the work rates of A and B be a,b resply. Work required to paint n rooms be W
So, W = a(t+1)
W = b(t)
So, a=bt/(t+1)
Also given that 3W/5 = (a+b)(4/3)
So, 3bt/5 = (bt/(t+1) + b)(4/3)
=>3t/5 = (4/3)(2t+1)/(t+1) => 9t(t+1) = 20(2t+1) => 9t^2 -31t -20 =>9t^2 -36t + 5t -20 = 0
So,(t-4)(9t+5) = 0
So, t=4
So, A takes 5 hours to finish n rooms.So, he takes 15 hours to finish 3n rooms.

Hence, E

bblast 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?

7
9
11
13
15


[spoiler]In the timed cat I tried algebraic approach which gave me an ugly quadratic mid way. Then i wasted another minute to plug choice C and D which was again difficult to solve. Try IT!!.

While reviewing later, I used a hybrid method to made a quadratic and then backsolved to E and obtained a solution.

But this aint any smart move. Even plugging involves a lot of time to solve this question.[/spoiler]

Math Gurus on this ?

We can plug in the answers, which represent the time it takes Albert to paint 3n rooms.
Given the denominators of the fractions included in the problem (3n/5 and 4/3), the correct answer is likely to be a multiple of 5 and 3.

Answer choice E: Albert takes 15 hours to paint 3n rooms.
Thus, to paint n rooms, Albert takes 15/3 = 5 hours.
Since Albert takes 1 hour longer than Bob, time for Bob = 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.

I came across a simlar question last night in a gmat club test :

Finally I would go with such an approach in these question : I don't wana remember the quadratic formula and I wana solve this quickly.

form the combined rate equation :

1/t + 1/(t-1) = 9/20.

= 20/t + 20/(t-1) = 9

plug answer choice E. since it says 15 hours for 3n work by Albert we need to plug 5 into the equation above as the equation above is the rate equation per unit work.

20/5 + 20/4 = 9 !!

also in this method we could easily eliminate answer choices A C and D as they are not divisible by 3 . similar question from gmat club test:

It takes Jack 2 more hours than Tom to type 20 pages. Working together, Jack and Tom can type 25 pages in 3 hours. How long will it take Jack to type 40 pages?

(A) 5 hours
(B) 6 hours
(C) 8 hours
(D) 10 hours
(E) 12 hours

E

IMO E
Another approach :
Applying RT=D (basic formula) , we get:
Rb(T) =n -------1 (Ra and Rb are rates of Albert and Bob,respectively)
Ra(t+1)=n -------2

Also given that (Ra+Rb)4/3 = 3n/5 -------3

As we know that we have relation between Ra and Rb from equation 1 and 2, and we can reduce equation 3 in Terms of Ra and work (3n ----> total work to be done by Albert) , we can rewrite equation 3 as :

(Ra+Ra(t+1)/t)(4/3) = 3n/5 => Ra[2+ (1/t)](20/3) = 3n

If you look at the bold part carefully, you will find that we are looking for the same in terms of Time.

A) [2+ (1/t)](20/3) = 7
1/t = (21/20)-2 (negative value) so not possible.

similarly all options will give 1/t --> negative except for option E

E) [2+ (1/t)](20/3) =15
1/t = (45/20)-2 = 5/20 = 1/4 ..Bingooo!!!

It takes Jack 2 more hours than Tom to type 20 pages. Working together, Jack and Tom can type 25 pages in 3 hours. How long will it take Jack to type 40 pages?

(A) 5 hours
(B) 6 hours
(C) 8 hours
(D) 10 hours
(E) 12 hours

j=t hours; tom=t-2
total = (t)(t-2)/(2t-2)
20 pages in (t)(t-2)/(2t-2)
25 in (t)(t-2)*5/(2t-2)*4 = 3
5t^2 - 10t = 24t-24
5t^2 - 34t + 24=0
5t^2 - 30t - 4t + 24 =0
t=6
thus to write 40 pages, 12 hours
E