Question

Mickey mows 1/3 of a lawn in 10 minutes. Minnie mows 1/4 of the lawn in 6 minutes. A student claims that Minnie is mowing faster because she only worked for 6 minutes, while Mickey worked for 10 minutes. Is the students reasoning correct ?

Answer 1

Mickey mows 1/3 of a lawn in 10 minutes.

So, his rate = (1/3) / 10 = 1/30 lawn/min

Minnie mows 1/4 of the lawn in 6 minutes.

So, his rate = (1/4) / 6 = 1/24 lawn/min

compare the fractions:

`\begin{gathered} (1)/(30)\text{ }(1)/(24)\text{ } \\ \end{gathered}`

Make the denominator are equal so, the common denominator is ( 30 x 24 = 720 )

So,

`\begin{gathered} (1)/(30)=(24)/(720) \\ (1)/(24)=(30)/(720) \\ So, \\ (30)/(720)>(24)/(720) \\ So,\text{ } \\ (1)/(24)>(1)/(30) \end{gathered}`

So, the rate of Minnie is faster than Mickey

This is because the rate of Minnie is greater than the rate of Mickey

So, the student reasoning is not correct