Time to fill tank using both pumps

Let the fixed emptying time be $t$ pm. Time taken by A alone $= 8 - t$ hours. Time taken by B alone $= 6 - t$ hours.

On Wednesday, A works for $(5 - t)$ hours and B works for $2$ hours (5 pm to 7 pm). Fraction of tank filled $= \frac{5-t}{8-t} + \frac{2}{6-t} = 1$.

Let $x = 8 - t$. Then $6 - t = x - 2$, and $5 - t = x - 3$. $\frac{x - 3}{x} + \frac{2}{x - 2} = 1$ $1 - \frac{3}{x} + \frac{2}{x - 2} = 1$ $\frac{3}{x} = \frac{2}{x - 2} \implies 3x - 6 = 2x \implies x = 6$

So $t = 8 - 6 = 2$ pm. Time taken by A alone $= 6$ hours. Time taken by B alone $= 4$ hours.

When both work together, time taken $= \frac{6 \times 4}{6 + 4} = \frac{24}{10} = 2.4\text{ hours} = 2\text{ hours } 24\text{ minutes}$. Starting at 2:00 pm, the tank will be full at 4:24 pm.