Work problem- previously posted, but don't understand- Help

Well, I was only able to solve it with brute force...

Printer B prints at a rate of 40/x pages per minute (ppm)

Printer A prints at a rate of 40/(x+4) ppm

We can set up an equation as follows:
(40/x)*6 + (40/(x+4))*6 = 50

If we simplify, we get a quadratic equation:
50x^2 - 280x - 960 = 0
It has two roots, x = 8, x = -2.4
The negative answer doesn't make sense, so our x is 8.

Now we can find the rate of printer A = 40/(8+4) = 3.33 ppm

Finally, 80/3.33 = 24


There has to be a much easier way, I just can't figure out it. If anyone can help me out, it'd be much appreciated. Thanks.

Set-up a table

Printer A B C
time x+4 x 6
pages 40 40 50
Rate 40/(x+4) 40/x 50/6


now we know rates are additive so:

40/(x+4) + 40/x = 50/6 = 25/3 which is approx 8.3

now we know printer A is SLOWER than printer B, so x/40 > half of 8.3 ~ 4.15

so if rate of B is around 5 then rate of A must be around 3.3, let's see if that works. BTW you can guess these numbers, knowing GMAT it likes to use whole numbers so guess 5, 6, 7 in that order.

so if 40/x=5 then x=8 and 40/(8+4)=3.3 --> no need to continue itterating, this one works

so now to print 80 pages we need 80/40*(x+4) = 2*(12) = 24

Takeaway - When combining work ask yourself which machine, person, thing doing work is faster. If they work as same speed then each item will output 0.5 of total (assuming there is 2). The faster machine will NECESSARILY produce MORE things in the same time as the slower machine - or conversely will take LESS time to produce the same amount of things as the slower machine.

Hope this helps

printer B 40 pgs say x min
then as per q printer A prints 40 pgs in x+4 min

both will print 40 pgs in = x*(x+4)/(x+x+4).....eqn1
(formula if A can do a job in x time and B in y time then together bth can do in x*y/(x+y))

now to prnt 40 pg ..tot time = eqn 1
to prnt 50 pgs =50/40 of eqn1..........eqn 2

tot time to prnt 50 pgs given is 6 min.....eqn 3

eqn2=eqn 3
i.e (5/4)*{x^2+4x}/{2x+4}=6

solving x = -12/5 or 8
x can not be a -ve value

so x+4=12(i.e time for A to prnt 40 pgs)

now for 40 pg time=12
for 80 pg time=80*12/40=24

hence ans is 24

hth

Is there a quicker way to solve the quadratic equation?

I kept getting stuck there.