Working alone at a constant rate, Machine A can produce 15 widgets in 2 minutes. Working alone at a constant rate, Machine B can produce 20 widgets in 3 minutes. If the two machines start working at the same time, after how many minutes will Machine A have produced 40 more widgets than Machine B?

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Working alone at a constant rate, Machine A can produce 15 widgets in 2 minutes. Working alone at a constant rate, Machine B can produce 20 widgets in 3 minutes. If the two machines start working at the same time, after how many minutes will Machine A have produced 40 more widgets than Machine B?