On a trip to the Grand Canyon Annie did a lot of hiking On h

On a trip to the Grand Canyon, Annie did a lot of hiking. On her two day hike, she discovered that 6 miles more than one half of the trip was the same as two-thirds the whol trip. What was the distances in miles that she traveled?

Solution

Let x=the whole trip
Then (2/3)x=two thirds of the whole trip
Also (1/2)x=half the whole trip
And (1/2)x+6=6 miles more than one half of the trip
Now we are told that:
6 miles more than one half of the trip was the same as two-thirds the whol trip.
So our equation to solve is:
(1/2)x+6=(2/3)x multiply both sides by 6 to get rid of fractions
3x+36=4x subtract 3x from both sides
3x-3x+36=4x-3x collect like terms
x=36 miles ------------the whole trip
(2/3)x=(2/3)*36=24 miles ----------------two thirds of the whole trip
(1/2)x=(1/2)*36=18 miles half the whole trip
6 miles more than one half of the trip=18+6=24 miles and this equals two thirds of the whole trip