Amazon Rainforest Its very dense. Almost impossible not to get lost without a guide. The mosquitoes there are relentless. Bring your strongest repellent if you ever visit. It was still wet season so much of the forest had to be explored by speedboat.
Tijuca Rainforest. This was the hike up to the Christ The Redeemer Statue in Rio, Brazil. A steep hike through a rainforest trail.
It is said to take 2 - 2 and 1/2 hours by walking. But it only took me an hour and 15 minutes. And this is with taking my sweet little time stopping to enjoy the view and take photos. Its a steep hike but i did see one person run. I would imagine running up would take maybe 40 - 50 minutes. You would have to do some climbing though.
Walking or running, i feel you would enjoy the hike. You seem like a hiker. Most take the van ride or tram to the statue. Hiking to the entrance is more adventurous and fun.