Question

Sylvia is hiking from Mineral Creek to Blueberry Hilla distance points of 6 1/5 miles. After hiking 2 2/3 miles , Sylvia stops for lunch. How much further does Sylvia have left to hike?

Answer Choices:

4 7/15
4 8/15
3 8/15
3 7/15

Answer 1

Given:

Total distance =
`6(1)/(5)` miles

Hiking before lunch =
`2(2)/(3)` miles

To find:

How much further does Sylvia have left to hike?

Solution:

Let x be the remaining hiking distance.

We know that,

Total hiking distance = Hiking before lunch + Remaining hiking distance

`6(1)/(5)=2(2)/(3)+x`

`((6* 5)+1)/(5)=((2* 3)+2)/(3)+x`

`(30+1)/(5)=(6+2)/(3)+x`

`(31)/(5)=(8)/(3)+x`

Isolate variable term.

`(31)/(5)-(8)/(3)=x`

`(93-40)/(15)=x`

`(53)/(15)=x`

It can be written as

`(45+8)/(15)=x`

`((3* 15)+8)/(15)=x`

`3(8)/(15)=x`

So,
`3(8)/(15)` miles left to hike.

Therefore, the correct option is C.