Rates and times per task -------------------
We can begin by solving the problem using rates—that is, the number of tasks completed per unit of time. Notice that the statement instead gives us the time required to complete one task. Rates and times per task are reciprocals. Since Line takes 2 h per task, her rate is (1/2) task/h. Similarly, since Maurice takes 3 h per task, his rate is (1/3) task/h.
Unlike times per task, rates have the useful property of being additive. In other words, the pair's rate is the sum of their individual rates. Here, then, their combined rate is 1/2+1/3 = 5/6 task/h. The time they take together to complete one task is found by taking the reciprocal once more, giving the answer: 6/5 h.
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