Question

Michael and his sister Mel share the job of mowing the grass in their yard. Michael mows 1/3 of the yard, and Mel mows the rest. Mel can mow 3/4 of the entire yard in an hour. 1. How long will it take Mel to finish mowing her part of the yard?2. After Michael mows 1/3 of the yard, what fraction of the yard does Mel need to mow? Explain.3. Write a fraction division problem that you can use to find out how long it will take Mel to finish mowing the yard.4. How long will it take Mel to finish mowing the yard? Show your work.

Answer 1

Michael mows 1/3 of the yard, and the remaining is for Mel,

Note that 1 whole yard is 1

So the remaining is 1 - 1/3 = 2/3

Mel can mow 3/4 of the entire yard in 1 hour :

So in 1 whole yard, Mel can mow it for :

`(1hr)/((3)/(4))=(4)/(3)hr\text{ per yard}`

Mel's rate in mowing 1 yard is 4/3 hrs

Since Mel will mow 2/3 of the yard, multiply it by her rate will be :

`(2)/(3)*(4)/(3)=(8)/(9)`

8/9 or 0.89 hour

Note that multiplication can be expressed as division,

The number of hours Mel can finish mowing the yard is :

`\begin{gathered} \text{hours}=\frac{\text{part of yard}}{\text{Mel's rate}} \\ \text{hours}=((2)/(3))/((4)/(3)) \\ \text{hours}=(8)/(9) \end{gathered}`

Since the answer is same, 8/9 hour is correct.

To summarize the answers :

1. 8/9 hr or 0.89 hr

2. 2/3, as explained above.

3. The division problem is :

`(2)/(3)/(3)/(4)`

4. 8/9 hr or 0.89 hr

`(2)/(3)/(3)/(4)=(2)/(3)*(4)/(3)=(8)/(9)`