Where is this character going at the end of Interstellar?

Question

Towards the end of the movie

Brand goes on to Edmund's planet while Coop and TARS complete their mission inside the event horizon of Gargantula.

Later,

Coop is spit out by "them" back in our galaxy, but close to 50 years have passed since they started the slingshot. Murph is old, and on her deathbed she tells Coop to go find Brand on Edmund's planet.

I don't understand what he expects to find there. Wouldn't

Brand also be much older, since decades passed for her too while Coop was inside the Tesseract?

Answer 1

He is going to Edmund's planet to meet up with Brand.

Brand has aged the same amount as Coop, because they both 'lost' an additional 51 years using the black-hole as a slingshot. Brand headed for Edmund's planet (which was several months away), while Coop plunged into the Event Horizon. Coop was then transported out of the wormhole near Saturn and picked up by the space station.

Now, you might say, because he was closer to the black-hole for longer (and inside it), Coop should have jumped even further into the future because of time dilation, but he clearly didn't (or this was adjusted by the future beings) because Murph was still alive when he got back to the Solar System. Murph was 10 when he left, they lost 23 years on the water world, and then lost 51 years using the black-hole, so Murph is at least 84 years old when Coop sees her again, and that is about the age she looks.

Answer 2

This is mentioned in a little more detail in the film's official novelisation. In short, due to his having being ejected from the Black hole (into Saturn orbit) at essentially the moment he entered it, her age remains pretty much the same as his:

He wondered how Brand was doing with that. How she was doing, period. Had she made it? The time dilation had been the same for them. As he popped out into space near Saturn, she was still on course to Edmunds’ world. She was either there, or would be soon. But when he considered everything she would have to accomplish, and all on her own, just to reach Edmunds’ World—the course corrections, placing the Endurance into a stable orbit. Loading the population bomb onto the lander—along with anything else she would ever need, since there wasn’t enough fuel to go back up once the lander had descended.

Answer 3

Following the logics of the film, there is no time distortion other then those experienced by both Brand and Cooper (on Millers and during the slingshot). The direct fall into the black hole by Cooper alone is not supposed to cause additional time loss in the film - you see that quite clearly when you listen to the dialogue between Romilly and Cooper on Manns planet: the plan to send TARS inside so that he can collect the data and try to figure out a way for transmitting the data is developped while they prepare for transport of camp and colony cargo down to Manns so that Cooper can leave on his journey home. The film does that by defining the hole as a "gentle" one - rotating in a way that something (TARS) crossing the horizon fast enough can survive that, so in the film the idea of crossing fast enough makes the difference - the slingshot in Gargantuans gravitational pull causes time distortion, a direct fast fall not. Otherwise sending TARS inside would be useless as getting the data millions or thousands or even hundreds of years (or even just further decades) later would be too late.

"They" (i.e. future "we") therefore do not transport Copper through time at the end, after closing the tesseract, just through space. Distortions inside the worm hole on his way back obviously cause a small time glitch which allows for the "handshake", but that's it, they don't choose a time for him to be found, just the space (near Saturn, where the space station is orbiting). Communication with the past via gravity was done inside of the tesseract, but this is communication only - he can "talk" with the past, not make himself a part of it - the entire sequence fall-tesseract-arrival at Saturn is written as one same time line, in which time passes for Cooper exactly as for Earth/Cooper station and as for Brand.

So, at the end, time is not additionally distorted, hours pass - those hours of oxygen that Cooper had in his space suit when he ejected from the shuttle inside the hole, he is found with minutes of oxygen left, that's the time that passed. When Cooper is found, Brand is still on her way to Edmunds planet. Murph was expected on the station "in a few weeks", in those few weeks (up to the talk between Cooper and Murph) Brand arrived on Edmunds planet, buried Edmunds, started to build the Camp up. So: exactly the same time has passed for both of them. Cooper will need a few weeks only to arrive on Endmunds planet (the space station orbits Saturn, so he is just nearby the worm hole, he does not have to travel additional 2 years this time and behind the hole is't a few weeks journey, that's all).

Answer 4

Those 51 years lost are before Coop enters the tesseract and after Brand is able to escape the black hole. So they both have the same amount of time lost at this point. For Coop being inside the tesseract, he exists outside of time at this moment, so, not time lost here.

The only real time difference that may occur, is when Coop waits for Murph to arrive on Cooper station, and that was “a couple of weeks.” Brand, for all we know, could have been in stasis unil she got to Edmund’s planet to preserve supplies and time. So, when Murph goes tells Coop to go after Brand, they’re still the same age, since they both experienced the same amount of time slippage from each ‘mission’ they did. Edmund’s planet isn’t affect by gargantua... yet... so Brand would be expereincing time as is on Earth. The only real difference in time is when Coop was waiting for Murph to arrive.

TL;DR: There’s probably only a few weeks different between Coop and Brand (not accounting for the possible time it takes to get to Edmund’s planet, which we don’t know.)