Problem:
Andy's lawn has twice as much area as Beth's lawn and three times as much area as Carlos' lawn. Carlos' lawn mower cuts half as fast as Beth's mower and one third as fast as Andy's mower. If they all start to mow their lawns at the same time, who will finish first?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let be the number of square feet in Andy's lawn. Then and are the areas of Beth's lawn and Carlos' lawn, respectively, in square feet. Let be the rate, in square feet per minute, that Carlos' lawn mower cuts. Then Beth's mower and Andy's mower cut at rates of and square feet per minute, respectively. Thus,
Andy takes minutes to mow his lawn,
Beth takes minutes to mow hers,
and
Carlos takes minutes to mow his.
Since , will finish first.
The problems on this page are the property of the MAA's American Mathematics Competitions