38 miles
Further explanation
<u>Given:</u>
A community bike ride offers a short 5.7-mile ride for children and families.
The short ride is followed by a long ride, 5²/₃ times as long as the short ride, for adults.
A woman bikes the short ride with her children, and then the long ride with friends.
<u>Question:</u>
How many miles does she ride together?
<u>The Process:</u>
Let us make a pattern for the short ride:
![\boxed{5.7} \rightarrow in \ miles](https://tex.z-dn.net/?f=%5Cboxed%7B5.7%7D%20%5Crightarrow%20in%20%5C%20miles)
Let us do a multiplication on a fraction at first.
![\boxed{ \ = \frac{2}{3} \times 5.7 \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20%3D%20%5Cfrac%7B2%7D%7B3%7D%20%5Ctimes%205.7%20%5C%20%7D)
![\boxed{ \ = \frac{2}{3} \times 5\frac{7}{10} \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20%3D%20%5Cfrac%7B2%7D%7B3%7D%20%5Ctimes%205%5Cfrac%7B7%7D%7B10%7D%20%5C%20%7D)
![\boxed{ \ = \frac{2}{3} \times \frac{57}{10} \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20%3D%20%5Cfrac%7B2%7D%7B3%7D%20%5Ctimes%20%5Cfrac%7B57%7D%7B10%7D%20%5C%20%7D)
We crossed out 3 and 57.
![\boxed{ \ = 2 \times \frac{19}{10} \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20%3D%202%20%5Ctimes%20%5Cfrac%7B19%7D%7B10%7D%20%5C%20%7D)
![\boxed{\boxed{ \ = 3.8 \ }}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cboxed%7B%20%5C%20%3D%203.8%20%5C%20%7D%7D)
Then we make a pattern for the long ride, 5²/₃ (five and two third) times as long as the short ride:
![\boxed{5.7}\boxed{5.7}\boxed{5.7}\boxed{5.7}\boxed{5.7}\boxed{3.8} \rightarrow in \ miles](https://tex.z-dn.net/?f=%5Cboxed%7B5.7%7D%5Cboxed%7B5.7%7D%5Cboxed%7B5.7%7D%5Cboxed%7B5.7%7D%5Cboxed%7B5.7%7D%5Cboxed%7B3.8%7D%20%5Crightarrow%20in%20%5C%20miles)
A woman bikes the short ride with her children, and then the long ride with friends. Let's calculate how many miles does she ride together.
- The short ride:
![\boxed{5.7 \ miles}](https://tex.z-dn.net/?f=%5Cboxed%7B5.7%20%5C%20miles%7D)
- The long ride:
![\boxed{(5.7 \times 5) + 3.8 = 28.5 + 3.8 = 32.3 \ miles}](https://tex.z-dn.net/?f=%5Cboxed%7B%285.7%20%5Ctimes%205%29%20%2B%203.8%20%3D%2028.5%20%2B%203.8%20%3D%2032.3%20%5C%20miles%7D)
![\boxed{ \ 5.7 + 32.3 = 38}](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%205.7%20%2B%2032.3%20%3D%2038%7D)
Thus, she rides 38 miles together.
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Keywords: A community bike ride, offers, a short 5.7-mile ride, for children and families, followed by, 5 2/3 times, for adults, a woman, with friends, how many miles, she ride together