OK, so your tank is, give or take, half a liter. Gasoline has an energy density of 34.2 MJ/L, so your tank would hold about 17.1 MJ of energy. Modern cars are about 30 to 35% efficient, I'm pretty sure that gas powered tools are much less energy efficient, but let's be reasonably generous and give it the 30%. With that, you end up with about 5.13 MJ of usable energy per tank of gas used.
Electric motors can get pretty darn close to 100% efficient. The best Lithium Ion batteries right now can get to 2.63 MJ/L. So you would probably need a battery that is roughly 2 Liters, 4 times the size of the original tank, that weighs 6 to 8 pounds, to match the 45 minute lifespan. So long as you can deal with the charging issue, You probably could go just about as long as you want trading off between 2 batteries of that size. If someone wanted to just go 8 hours on one charge, you would be looking at some type of heavy battery backpack that would be at least 20 liters, and 60 to 80 pounds, probably too heavy.