Since in 8 hours the experienced clerk can fill the entire order, in 1 hour he can fill 1/8 of the order. Similarly, since in 9 hours the new clerk can fill the entire order, in 1 hour he can fill 1/9 of the order. Thus, working together, in 1 hour the 2 clerks can fill 1/8 + 1/9 = 9/72 + 8/72 = 17/72 of the order. If they work for x hours, the fraction of the order they can fill is (17/72)*x. Thus, we can set this fraction equal to 1 (which would represent the entire order), and solve for x:
(17/72)*x = 1. Multiplying both sides by 72/17 gives us (72/17)*(17/72)*x = (72/17)*1, so x = 72/17 = 4 4/17 = 4.24 hours.
