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

`7(3)/(8) \ miles`

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(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(1)/(8) =x+6(3)/(4) \\ (14*8+1)/(8)=x+(6*4+3)/(4) \\(113)/(8) =x+(27)/(4)`

Subtracting both side by
`(27)/(4)`

`(113)/(8) -(27)/(4) =x+(27)/(4)-(27)/(4)`

Taking LCM of 4 and 8 ,we get 8

`(113-54)/(8) =x\\\\(59)/(8) =x\\\ \\7(3)/(8) = x`

Therefore, the friends walk before lunch is
`7(3)/(8) \ miles`.