2001 CEMC Gauss (Grade 8) Problems/Problem 10

Problem

Rowena is able to mow $\frac{2}{5}$ of a lawn in $18$ minutes. If she began the job at $10:00 \text{ a.m.}$, and mowed at this same constant rate, when did she finish mowing the entire lawn?

$\text{ (A) }\ 10:08 \text { a.m.} \qquad\text{ (B) }\ 11:30 \text{ a.m.} \qquad\text{ (C) }\ 10:40 \text{ a.m.} \qquad\text{ (D) }\ 10:25 \text{ a.m.} \qquad\text{ (E) }\ 10:45 \text { a.m.}$

Solution 1

Let $m$ be the number of minutes that it takes for Rowena to mow $1$ whole lawn. We then have:

$\frac{2}{5} \times m = 18$

$m = 18 \div \frac{2}{5} = 18 \times \frac{5}{2} = 45$ minutes

Since it takes $45$ minutes to mow the lawn, she would have finished $45$ minutes after $10:00 \text{ a.m.}$ Thus, she finished at $\boxed {\textbf {(E) } 10:45 \text { a.m.}}$

~anabel.disher

2001 CEMC Gauss (Grade 8) (ProblemsAnswer KeyResources)
Preceded by
Problem 9
Followed by
Problem 11
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CEMC Gauss (Grade 8)