Question

Travis is mowing his yard and his sister is raking up the grass behind him. By lunch time, he has mowed 1/2 of his yard. His sister has raked 1/3 of what he’s mowed. How much of the yard has been mowed and raked?

Answer 1

Let's denote the total area of the yard as \( Y \).

Travis has mowed \( \frac{1}{2}Y \) of the yard by lunch time.

His sister has raked \( \frac{1}{3} \) of what he has mowed. Since he mowed \( \frac{1}{2}Y \), the amount that his sister has raked is:

\[
\frac{1}{3} \times \frac{1}{2}Y = \frac{1}{6}Y
\]

Now, to find the total amount of the yard that has been mowed and raked together, we add the area mowed by Travis and the area raked by his sister:

\[
\text{Total mowed and raked} = \frac{1}{2}Y + \frac{1}{6}Y
\]

To add these fractions, we need a common denominator. The least common denominator of 2 and 6 is 6.

Rewriting \( \frac{1}{2}Y \) in terms of sixths:

\[
\frac{1}{2}Y = \frac{3}{6}Y
\]

Now we can add the two fractions:

\[
\frac{3}{6}Y + \frac{1}{6}Y = \frac{4}{6}Y
\]

This simplifies to:

\[
\frac{4}{6}Y = \frac{2}{3}Y
\]

Therefore, the total area of the yard that has been mowed and raked is

\[
\frac{2}{3} \text{ of the yard.}
\]