on a typical day, the trapeze artist spends 1/2 of his time plotting his jumps and 1/4 of his time hoping he won't fall. if the trapeze artist spends a total of 6 hours on these two activities, how many hours does he typically work each day?
Let's say the total time the trapeze artist spends on these activities is represented by T.
The trapeze artist spends 1/2 * T plotting his jumps.
He also spends 1/4 * T hoping he won't fall.
The total time spent on these activities is 1/2 * T + 1/4 * T = 6.
Multiplying through by a common denominator of 4, we get 2 * T + T = 24.
Combining like terms, we get 3 * T = 24.
Dividing both sides by 3 gives T = 8.
So typically, the trapeze artist works for 8 hours each day. Answer: \boxed{8}.