Question

Quantavius took a hiking with some friends.The friend started early and walked a while before stoping to each lunch.After lunch the friends walked 6 3/4 miles before arriving at the end of the trail .The trail is 14 1/8 miles long.How long did the friends walk before lunch

Answer 1

Answer:

$7\frac{3}{8} \ miles$

Step-by-step explanation:

Given:

After lunch the friends walked 6 3/4 miles before arriving at the end of the trail.

The trail is 14 1/8 miles long.

Question asked:

How long did the friends walk before lunch ?

Solution:

Let the friends walk before lunch in miles = $x$

As total length of trail is given $14\frac{1}{8}\ miles$ , we can conclude:

Total length of trail = The friends walk before lunch in miles  + The friends walk after lunch in miles

$14\frac{1}{8} =x+6\frac{3}{4} \\ \frac{14\times8+1}{8}=x+\frac{6\times4+3}{4} \\\frac{113}{8} =x+\frac{27}{4}$

Subtracting both side by $\frac{27}{4}$

$\frac{113}{8} -\frac{27}{4} =x+\frac{27}{4}-\frac{27}{4}$

Taking LCM of 4 and 8 ,we get 8

$\frac{113-54}{8} =x\\\\\frac{59}{8} =x\\\ \\7\frac{3}{8} = x$

Therefore, the friends walk before lunch is $7\frac{3}{8} \ miles$.