Final answer:
By working together, two workers with individual task completion times of m minutes and 9m minutes respectively can complete one task in 9/10m minutes.
Step-by-step explanation:
If one worker can complete a task in m minutes, and a second worker can complete the same task in 9m minutes, we need to determine how long it would take both workers to complete the task if they worked together.
To solve this, we'll let the work done by the first worker be 1 job per m minutes (which is the same as 1/m jobs per minute), and the work done by the second worker be 1 job per 9m minutes (which is the same as 1/(9m) jobs per minute).
When they work together, their combined work rate is:
(1/m) + (1/(9m)) = (9/9m) + (1/9m) = (9+1)/(9m) = 10/(9m) jobs per minute.
To complete 1 job, we then find the time (t minutes) by setting the combined work rate equal to 1 job:
1 job = (10/(9m)) jobs per minute × t minutes
Solving for t, we find:
t = (9/10)m minutes
Thus, by working together, the two workers can complete the task in 9/10m minutes.