My general rule is 30 minutes per mile plus 30 minutes per 1,000' gained. Trail Camp to summit is about 5 miles plus 2,500', so my rule of thumb would say about 3-1/2 to 4 hours. Trouble is, my thumbs slow down above 12,000', so it took Nathan and me a shade over 5 hours (0530 - 1045) when we
hiked up Whitney in '01. The weather was closing in as we came down and we had to stop to put on rain gear, so it took us close to 4 hours on the way down, as well, but that was counting some weather-related delays. (Nathan was 12, I was 50)
A few years later, we did Elbert over in CO as a dayhike. Same 5 miles but closer to 5,000' gained and that one we did in a similar 5-plus hours up. By then, of course, he was taller than I but even now (he's 6'2", I'm 5'8") I'll walk away from him above 12,000'. He hasn't learned to pace himself (yet) at altitude. Once he does, I'll be eating his dust the whole way up...
As they say, your mileage may vary...