If they all start to mow their lawns at the same time then Beth's mower will finish first.
Let area of Beth's lawn = x
area of Carlos' lawn = y
Andy's lawn has twice as much area as Beth's lawn and three times as much as Carlos' lawn. So, we can write
area of Andy's lawn =2x = 3y equation 1
Carlos' lawn mower cuts half as fast as Beth's mower and one third as fast as Andy's mower
Let, speed of Beth's mower = z
and speed of Andy's lawn mower = k
speed of Carlos' lawn mower = z/2 = 1/3k equation 2
area of Beth's lawn = x
area of Andy's lawn =2x
area of Carlos' lawn = 2x/3 = 0.66x (Using equation 1)
speed of Beth's mower = z
speed of Andy's lawn mower = 3z/2 = 1.5 z (using equation 2)
speed of Carlos' lawn mower = z/2 = 0.5 z
Time = area / speed
Ratio , Beth : Andy : Carlos
[tex]\frac{x}{z} :\frac{2x}{3z/2} :\frac{2x/3}{z/2}[/tex]
On simplification, we get
1 : (4/3) : (4/3)
1 : 1.33 : 1.33
From the ratio be can clearly see that Beth's mower will finish first.
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