tA + tB is not the same as t(A+B)
You can add rates when machines work together, not time
Imagine if a printer prints 10 pages per minute
If we use two printers we will have 20 pages per minute
The time taken to print has reduced not increased
Coming back to the problem:
rA/rB = 3/2
rB = 2 rA/3
r(A+B) = 1/t(A+B) = 1/4
r(A+B) = r(A) + r(B) = 1/4
r(A) + 2 rA/3 = 1/4
5 rA/3 = 1/4
rA = 3/20
tA = 1/rA = 20/3