How long would it take for a silghtly broken leg to heal ?

Here's a good source (listed below). Slightly broken may mean greenstick, incomplete, or in the case of the lower leg, a fracture of the fibula but not the tibia. So there's no way to totally answer the question. Also, if you smoke it significantly slows healing time. You can learn a lot from the website. Take care of yourself and you will heal up just fine. Your leg will likely look skinny when it first comes out of the cast but it will bulk up quickly.

It depends which bone is broken, and where.

n general, small broken bones with simple fractures take about four weeks to heal in small children. In teenagers and adults, small bones — like a finger or wrist bone — with a simple fracture, will take about six weeks to heal. Larger broken bones, for example the bones in the thigh, would take a great deal longer to heal, usually six weeks to three months in the average healthy adult. So it certainly does not appear at all likely that it will be off by September 7th. However look at the good side you will be able to get all your friends to autograph the cast so that will become a positive.