a new 5 mile nature trail is 125% of the length of the original trail.How long is the original trail?
5 = 1.25 x
x = 4
To find the length of the original trail, we can use the concept of proportions. Let's set up a proportion to solve for it.
Let x be the length of the original trail.
According to the information given, the new nature trail is 125% (or 1.25) of the length of the original trail. So, the length of the new trail is 1.25x.
Now, we can set up the following proportion:
1.25x / x = 5 miles / y
In the proportion, y represents the length of the new trail, which is given as 5 miles.
Simplifying the proportion, we have:
1.25x / x = 5 / y
To solve for x, we can cross-multiply:
1.25x * y = 5 * x
Now, substitute the given values:
1.25x * 5 = 5 * x
Multiply:
6.25x = 5x
Subtract 5x from both sides:
6.25x - 5x = 0
1.25x = 0
Divide both sides by 1.25:
x = 0
Therefore, the length of the original trail is 0 miles.