Problem Solving

Two pipes A & B can fill a swimming pool at a consant rate in 60 hours, 40 hours, or 24 hours, depending on whether pipe A alone, pipe B alone, or both pipes are used. If the pool is filled by using pipe B alone for half the time and both pipes for half the time, how many hours does it take to fill the pool?


Now i know sort of how to solve this problem, but the solution explanation throws me off and I get the problem wrong obviously.

usually work problems are sovled by an equation much like the following right?

time/job1 + time/job2 = 1 <--- one being the whole job

so wouldnt this problem be solved like this?:


1/40 (for pipe b) + 1/24 (for both) = X <--- being the time for both combinations to fill the pool

right?


but the solution set says that this is the formula:


.05t/40+.05t/24=1

I dont quite get that problem

okay so the =1 is the whole pool, I get that

obviously .05 isnt the half the time it takes to fill the pool either? That would be .5

so where did the .05t come from?