Question

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?

Andy

Beth

Carlos

Andy and Carlos tie for first.

All three tie.

Solution:

Let Andy's lawn have area $A,$ so Beth's is $\dfrac{A}{2}$ and Carlos' is $\dfrac{A}{3}.$ Let Carlos mow at rate $R,$ so Beth mows at $2R$ and Andy at $3R.$

The times are $\text{Andy: } \dfrac{A}{3R}, \quad \text{Beth: } \dfrac{A/2}{2R} = \dfrac{A}{4R}, \quad \text{Carlos: } \dfrac{A/3}{R} = \dfrac{A}{3R}.$

Since $\dfrac{A}{4R}$ is the smallest, Beth finishes first.

Thus, the correct answer is B.

2002 AMC 10B Problem 21

Solution:

Problem 21 in Other Years