Mowing Lawns
Abby can mow a particular lawn in 6 hours, but Betty can do it in only 4 hours. If Abby and Betty work together, how many minutes would it take them to mow the lawn?
Details and assumptions
Assume Abby and Betty both have their own lawn mowers, and they won't get in the way of each other.
The answer is 144.
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1 solution
Solution 1: Abby mows at 1/6 lawn per hour; Betty mows at 1/4 lawn per hour. Together they mow at 5/12 lawn per hour, so they can mow 1 lawn in 12/5 hours, which is 5 1 2 × 6 0 = 1 4 4 minutes.
Solution 2: Betty works 50% faster than Abby. Together they work 2.5 times faster than Abby alone. Since Abby can mow the lawn in 6 hours, together they can mow the lawn in 6/2.5 hours, or 2 . 5 6 × 6 0 = 1 4 4 minutes.
Solution 3: Divide the lawn into 12 equal parts. In two hours, Betty will mow 6 parts and Abby will mow 4. In the remaining part, Betty will mow 3/5 and Abby will mow 2/5; and it will take them 2/5 hour to mow this last part. Together they will take 2 + 2/5 hours = 144 minutes.