Question

At a furniture manufacturer, worker A can assemble a shelving unit in 5 hours. Worker B can assemble the same shelving unit in 3 hours. Which equation can be used to find t, the time in hours it takes for worker A and worker B to assemble a shelving unit together?


Rate
(Shelving Units per Hour)
Time
(Hours)
Fraction Completed
Worker A
One-fifth
t

Worker B
One-third
t


5 t + 3 t = 1
One-fifth t minus one-third t = 1
One-fifth t + one-third t = 1
5 t minus 3 5 = 1

Answer 1

Worker A does (1/5) unit/hour and B does (1/3) unit/hour, so together in t hours they do (1/5)t + (1/3)t. Set that equal to 1:

(1/5)t + (1/3)t = 1.

(If solved, t = 1 ÷ (1/5 + 1/3) = 15/8 = 1.875 hours.)