A rate expresses one quantity per unit of another, such as kilometers per hour or tasks per minute. Work problems become clearer when you convert completion times into rates before combining them.
Combine rates for a shared task
Machine A completes one job in six hours. Machine B completes the same job in three hours. If they work independently at constant rates on a divisible shared job, A completes 1/6 of a job per hour and B completes 1/3.
Together their rate is 1/6 + 1/3 = 1/2 job per hour. The shared job takes two hours. Adding six and three would combine durations, not output rates.
Keep the assumptions visible
The calculation assumes the machines can contribute simultaneously without interfering and that their rates remain constant. If the task cannot be divided or requires sequential steps, the same formula may not apply.
Reasoning questions often state simplifying assumptions. Use them, but do not silently transfer them to a different scenario.
Distance and time
A traveler covers 90 kilometers in 1.5 hours. The average speed is 90 ÷ 1.5 = 60 km/h. Converting 90 minutes to 1.5 hours is essential if the requested unit is kilometers per hour.
If the traveler spends equal time at two speeds, averaging those speeds is appropriate. Equal distances do not generally justify the same shortcut, because the slower segment takes longer.
Try a production example
Three identical printers produce 180 pages in six minutes at a constant rate. Their combined rate is 30 pages per minute, so each produces ten. Five such printers would produce 200 pages in four minutes, assuming the same operating conditions.
Check units at each step
Write quantity divided by time to obtain a rate, then multiply a rate by time to recover output. If the units do not cancel in the intended way, revisit the setup before doing more arithmetic.