Most of those BTU/hr are about speed of the melt. A Lee 10 lb pot has a 500 Watt heating element. 500W=1,706 BTU/hr. If 1,706 BTU/hr will melt 10 lbs in a reasonable time, then 5 times that (8530 BTU/hr) will melt 50 lb in the same reasonable time if the coupling to the heat source is as good. Once hot, because the larger mass has less surface area per unit weight, it will actually take even less to keep it melted. So, the melting can be done with under 10,000 BTU/hr. The rest is gravy for speed.
Boiling water: lbs of water times degrees of temperature rise needed to reach boiling = BTU's, total. 50 gallons is about 417 lbs. If you raise the temperature from 75°F to 212°F, with a BTU raising a pound of water one degree, that will be 417 lbs × 137 degrees difference × 1 BTU/lb-deg, or 57,162 BTU's. So that's how many BTU's you have to put into the water. How long that takes to do depends on how many BTU per hour the heater puts out, + BTU's for heat lost to to the air or never fully put into the pot during the heating. If you suppose the open flame loses a third of its heat to the air, then a 15,000 BTU/hr burner would put about 10,000 BTU/hr into the pot, so it would take 57,162 BTU/10,000 BTU/hr = 5.7162 hr, or five hours and 43 minutes to reach the boiling point.
It won't work out that smoothly, because loss rate to the air increases as the pot heats up, but you get some sort of ballpark idea this way.