Multiple-millions of years for the Grand Canyon. Same for wearing out mountains.
Note: The mountain range right along the Red River (the Southern boundary of the state of Oklahoma, with Texas being just on the other side) in the USA? Used to be one of the highest on earth.
How can they tell? Well-- scientists examined the rocks in what is now a modest set of hills, really, and compared them to sediment drilled up from the mouth of the Mississippi River. Sonar mapping and other methods, has mapped out the entirety of the Mississippi River Delta (and what's underneath the ocean's surface)
A lot of that delta? Came from what used to be high mountains in Oklahoma/Texas. Rain poured on them for multiple millions of decades, washing it down to the Mississippi River, via the Western Mississippi Watershed.
The rocks in what's left of those mountains, matches a lot of the sediment in the Delta.
Calculating the volume of sediment can give a pretty good guess on how high those mountains used to be.
Yes-- it's not Rocket Science. But it
is Geology.