x=small pump rate y = large pump rate
4y + 2x = Swimming pool (in 2 hours) = 1 pool/2hr
AND:
2 y + 6x = swimming pool (in 2 hours) = 1 pool/2hr
From the first equation 2x = 1/2 - 4y
x = 1/4-2y substitute this into the second equation
2y + 6 ((1/4-2y) = 1/2 Solve for y
2y + 6/4 -12y = 1/2
-10y = -1
y = 1/10 pool/ hr Sub this into 1st(or 2nd) equation:
4(1/10) + 2x = 1/2 solve for x = 1/20 pool/hr
Now : for the final part of the question.....
( 8(y) + 8(x)) t = 1/2 pool
( 8(1/10) + 8(1/20) ) t = 1/2
(16/20 + 8/20) t = 1/2
( 24/20 ) t = 1/2
t = 1/2 * 20/24 = 20/48 hr = 20/48*60 = 25 mins