Joe gets paid $20 per hour for his work as a human billboard, and this week, with the elections so near, he plans to work 10 hours overtime. By week's end, the government will have taken out $240 in taxes from his check, leaving him a total of $760. How many hours does Joe normally work per week?
Let x be the number of hours Joe normally works per week.
Joe earns 20 * x dollars normally.
This week, Joe earns 20 * x + 20 * 10 = 20x + 200 dollars.
Joe's total earnings after taxes are 20x + 200 - 240 = 20x - 40 dollars.
20x - 40 = 760
20x = 800
x = <<40=40>>40
Joe normally works 40 hours per week. Answer: \boxed{40}.