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Math and Logic

How Much Faster Together?

Suppose you and a friend can each dig a 20-foot ditch by yourselves in 3 hours. How long would it take you to dig the ditch working together, assuming you both have enough room to work without getting in each other's ways?

A little reasoning tells us that the project should get finished in half the time since you're doubling your efforts by combining forces, so it should take 1121\frac12 hours to dig the ditch.

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