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 = $6\dfrac{1}{5}$ miles

Hiking before lunch = $2\dfrac{2}{3}$ 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

$6\dfrac{1}{5}=2\dfrac{2}{3}+x$

$\dfrac{(6\times 5)+1}{5}=\dfrac{(2\times 3)+2}{3}+x$

$\dfrac{30+1}{5}=\dfrac{6+2}{3}+x$

$\dfrac{31}{5}=\dfrac{8}{3}+x$

Isolate variable term.

$\dfrac{31}{5}-\dfrac{8}{3}=x$

$\dfrac{93-40}{15}=x$

$\dfrac{53}{15}=x$

It can be written as

$\dfrac{45+8}{15}=x$

$\dfrac{(3\times 15)+8}{15}=x$

$3\dfrac{8}{15}=x$

So, $3\dfrac{8}{15}$ miles left to hike.

Therefore, the correct option is C.