It takes a minimum of 3 1/2 hours to get to Machu Picchu from Cusco; an hour and a half by car, van or bus to Ollantaytambo and an hour and a half by train from there to Aguas Calientes. Then there there is a half hour bus ride to the citadel. You should probably allow a minimum of another 15 to 20 minutes for each connection.

The train from the outskirts of Cusco to Aquas Calientes takes over four hours.

If you get to Cusco the night before and get started very early, in time to catch the 6:00 am train from Ollantaytambo to Aguas Calientes, you should be able to spend a few hours at the citadel and return to Cusco in time to catch a late flight to Lima. It's going to be a very long day.