Related rates ladder problem, what is wrong with my algebraic solution?

Question

So while reading the solution (which uses implicit differentiation) of the following related rates ladder problem I thought about the algebraic way of solving it, but it gives wrong result so I want to know what is wrong with it. The problem is this "A ladder 10 feet long rests against a vertical wall. If the bottom of the ladder slides away from the wall at the rate of 1 ft/s. How fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 ft from the wall ?". So my algebraic solution is this, till the end of the ladder's fall bottom must go 4 feet, so it will do it in 4 seconds, and this means that the top of the ladder goes down with the speed of 2 ft/s (because height is 8 ft by pythagorean theorem). But the right answer is 3/4 ft/s. So I think the fault in my solution is the assumption that velocity is constant, so is it? If not, what is the reason for this ?