Hello PHMTY. We use reciprocals, when dealing with 'combined work rates' type problems. See
this page, for some worked examples.
For example, if it takes me 15 minutes to complete a task, then I complete 1/15th of the job per minute. (1/15 is the reciprocal of 15.) If it takes you 10 minutes to complete the same task, then you complete 1/10th of the job per minute. (1/10 is the reciprocal of 10.) We add the reciprocals, to find the fractional amount of the task completed per time unit when we work together.
1/15 + 1/10 = 1/6
In other words, working together, we complete 1/6th of the task per minute. That means it takes us 6 minutes, working together. (6 is the reciprocal of 1/6.)
Go through some worked examples, at the link above. See if that helps. Post your attempt, if you'd like more help.
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