I am sorry I misunderstood you. It looks like you are saying that the source and the receiver are both moving at 10 km/sec. That is a very simple question. It would take exactly 1 second from the source to the receiver and it would take exactly 1 second to return. Both the source and the receiver are in the same inertial frame so they both would agree on the time and distance the light traveled. Consider this. Assume you wake up on what appears to be an airplane but your not sure how or why you are there. Is there any test you can do (other than looking out the window) that will prove that you are either flying at 500 mph or that you are on the ground and you are being tricked into thinking you are flying? In other words are you moving at 0 mph or 500 mph.
If the sender and receiver are stationary with respect to each other, there is no change in frequency. If your relative speed changes (or, to use your words, your "perspective") then you will see a change in the content of the light (both energy and frequency. Michelson Morley proves that there is no fixed, or preferred, reference frame; the only thing that matters is relative speed. To put it another way, there is no absolute speed referenced to some sort of "zero speed" field (often referred to as the ether.)
Aaand that's how it happens. Some people wish to stay wilfully ignorant about the things they like to think about but don't wish to learn about. So they enthusiastically go down blind alleys, pursuing woefully flawed thinking.
The idea that time changes is counter intuitive. I have accepted that that is what the experiments show, but still have to grapple with the implications.