Albert and Bob are painting rooms at constant, but different

Hi,

This question can be done very quickly if you understand what they asking for.

I will present a very general way of solving ANY work,rate and time related question:

Question will always ask for something out of rate or time or work. (obviously coz its a work time rate related question )
ex. in this question they want "time" for "3n" work done by Albert, right??
This means ------> rate * TIME = 3n =====> All you have to do it find out the RATE for albert and then put it here to find the TIME!!!!! (easy right??)

Let see what is given here:
some relation between Albert and bob's individual time
and their combined time.

In combined time: some work and time is given, we don't care what it is, all we will do is find their rate by writing WORK/TIME
i.e. (3n/5) / 4/3 = 9n/20 = 9/20

From individual relationships just find Albert and Bob's respective rates:
A: takes 'a' time to complete n rooms===> rate becomes : n/a = 1/a
B: takes 1 hr less than A to complete n rooms =====> rate becomes : n/(a-1) = 1/a-1

now add individual rates and equate 'em to the combined rate:

1/a + 1/(a-1) = 9/20
From my experience I feel that from thus point its faster and much easier to put values than solve the quadratic:
if u see that answer I feel 9 and 15 stand out as they are multiples of 3 and they represent 3n work, we can do 3n=15 => n = 5 and put "5" in place of "a" in the equation. it will be equal to 9/20 thats ur answer.

BOTTOM LINE: first thing always look for what is need to in final answer and how can I get their, if yo start by what's given then u will start doing actions not even necessary to reach the solutions.

I hope this helps,

thanks,

-Kartik