SOLUTION: One grocery clerk can stock a shelf in 30 min. A second cleck requires 45 min to stock the same shelf. How long would it take to stock the shelf if the two clerks worked together?

Question 1176251: One grocery clerk can stock a shelf in 30 min. A second cleck requires 45 min to stock the same shelf. How long would it take to stock the shelf if the two clerks worked together?
Found 2 solutions by CubeyThePenguin, greenestamps:
Answer by CubeyThePenguin(3113) (Show Source): You can put this solution on YOUR website!
clerk A: 1/30 of the shelf stocked in 1 minute
clerk B: 1/45 of the shelf stocked in 1 minute

together: 1/x of the shelf stocked in 1 minute

1/30 + 1/45 = 1/x

x = 18 minutes
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

Here is an alternative to the standard algebraic method for solving problems like this as shown by the other tutor.

The least common multiple of the two given times is 90 minutes.

In 90 minutes the first clerk could stock 90/30 = 3 shelves; the other could stock 90/45 = 2 shelves.

So together in 90 minutes the two clerks could stcok 3+2=5 shelves; that means they can stock the one shelf if 90/5 = 18 minutes.

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