Tina can weed her vegetable garden completely in 70 minutes. Her friend Marisa can do the same task in 40 minutes. If they work together, how long does it take Tina and Marisa to weed the vegetable garden?
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To find out how long it takes Tina and Marisa to weed the vegetable garden together, we can use the concept of work rates.
First, let's calculate their individual work rates. Tina can weed the garden in 70 minutes, so her work rate is 1/70 of the garden per minute. Marisa can do the same task in 40 minutes, so her work rate is 1/40 of the garden per minute.
When they work together, their work rates are added up. So their combined work rate is (1/70 + 1/40) of the garden per minute.
To find out how long it takes them to weed the entire garden together, we need to invert their combined work rate. So the total time will be the reciprocal of their combined work rate.
Let's calculate it:
Combined work rate = 1/70 + 1/40 = (4/280 + 7/280) = 11/280 of the garden per minute.
Total time = reciprocal of the combined work rate = 280/11 minutes.
Therefore, Tina and Marisa will take approximately 25.45 minutes to weed the vegetable garden together.