If a 5 metre ladder is resting against a wall and the bottom of the ladder is 3 metres away from the wall, and someone pulls the bottom of the ladder away at a speed of 1 metre per second, calculate the speed of the top of the ladder after t seconds

After t seconds the distance between the bottom of the ladder and the wall is t metres. Let x denote the distance that the top of the ladder has moved after t seconds. Now use the theorem of Pythagoras to obtain a quadratic equation in x and t. Then use implicit differentiation to obtain a formula for dx/dt in terms of x and t, and solve the quadratic to express this in terms of t alone.