Translating for numbers, we have:
![(1)/(5)=0,2\rightarrow3(1)/(5)=3,2](https://img.qammunity.org/2023/formulas/mathematics/college/707trna4bzmr0oifn61n0hzqc5hsum73zf.png)
This way, we can make what follows:
![Day_1+Day_2=3(1)/(5)+4=3,2+4=7,2_{}](https://img.qammunity.org/2023/formulas/mathematics/college/lrh5cvmw1szvmis0fzwgmk2i4ztxwbjd97.png)
Calculating now the amount is needed to complete the 9 miles:
![Day_3=9-7,2\text{ = 1,8}](https://img.qammunity.org/2023/formulas/mathematics/college/qhb6e16gug6dsoilc5xksdt86xbiblf060.png)
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And from here, the solution with the fractions.
We can start with the sum of what Shelly has biked in the first two days:
![Day_1+Day_2=3(1)/(5)+4=7(1)/(5)_{}](https://img.qammunity.org/2023/formulas/mathematics/college/hsj0nylsrsencj1lecm6rc3b11wmmian1p.png)
This is the amount of mile she has already biked. But we know she needs to complete all the 9 miles in the third day. So, the difference from 9 and the amount she already did is the amount she needs to bike in the third day.
![\text{Day}_3\text{ = 9 - 7}(1)/(5)\text{ = 1}(4)/(5)](https://img.qammunity.org/2023/formulas/mathematics/college/n5meijg6le8d6pbp0um5a6xs7ycwopr13j.png)