How fast was Apollo 11 going?

Asking for "the" speed of Apollo 11 is a trick question, because it kept changing throughout the entire trip. After liftoff, the spacecraft was left in a parking orbit around Earth; then the Saturn V's upper stage reignited for 5 minutes and 48 seconds to put the stack on a trans-lunar trajectory. From that moment it kept losing speed as it climbed out of Earth's gravity well, and regained it as it fell toward the Moon.

On arrival, the service module's engine had to do just the opposite: slow down. A retrograde burn of 357.5 seconds left the spacecraft in an elliptical lunar orbit of 69 by 190 miles. The Eagle's descent was another braking exercise, with the engine firing for 756.3 seconds until it touched down in the Sea of Tranquility. Every maneuver of the flight was, in essence, a speed adjustment measured in seconds of burn time.

The figure NASA states explicitly corresponds to the return trip. The command module Columbia entered Earth's atmosphere at 39,000 km/h (24,000 mph). At that speed the air doesn't have time to move out of the way: it compresses in front of the heat shield, and the surrounding gas exceeds 5,000°F, enough to turn the capsule into a fireball with a trail of glowing plasma.

The atmospheric braking was as violent as it was brief. About nine minutes after reentry began, the three main parachutes opened, slowing the capsule to about 25 miles per hour (mph), little more than a jog. At that pace it touched down in the Pacific Ocean on July 24, 1969, at 16:50:35 UT. All the energy built up on the way home had been dissipated as heat and disturbed air within a matter of minutes.