A printing order is measured as 5,400 impression-units. Machine P turns out 45 units an hour, machine Q 30 units an hour and machine R 15 units an hour. P and Q run together for the first 24 hours, after which Q is withdrawn for servicing and R takes its place. How many hours does the whole order take?

P and Q together produce 75 units an hour, so 24 hours give 1,800 units and 3,600 remain. P and R together produce 60 units an hour, needing 3,600 ÷ 60 = 60 hours. Total 24 + 60 = 84 hours. 60 hours quotes only the closing stretch. 72 hours runs the whole 5,400 units at the opening pair's 75 an hour. 90 hours runs the whole order at the closing pair's 60 an hour, ignoring the faster opening 24 hours.