One More Training Run

An image-tagging model cost $60{,}000$ dollars of GPU time to train. In production it handles $200{,}000$ requests a day, every day, and serving costs $0.002$ dollars per request.

An engineer proposes distilling it into a smaller student:

• producing the student takes one more training run, costing $24{,}000$ dollars;
• the student has been checked, and is accurate enough to replace the current model outright;
• serving the student costs 60% less per request.

The model is expected to stay in service for years. Counting from the day the student takes over, after how many days have its savings paid for the extra training run?