Final answer:
A delay exists because radio waves traveling at the speed of light take 1.3 seconds to reach the Moon from Earth, making a round trip of approximately 2.6 seconds.
Step-by-step explanation:
The reason why there is a delay between the time a radio transmission is sent and when it is received by astronauts on the Moon is because of the finite speed at which electromagnetic waves travel. These waves, which include radio waves, travel at the speed of light, which is approximately 300,000,000 meters per second (3 × 108 m/s) in a vacuum. The Moon is about 384,400 kilometers away from Earth on average. Since the radio waves take time to cover this distance, there is an inevitable delay. Specifically, it takes light or radio waves 1.3 seconds for a one-way trip from Earth to the Moon. So, a round trip, which is the time required for Mission Control to send a message to the astronauts and receive a response, takes about 2.6 seconds, resulting in the observed delay.