Rachel had high 2/3 of the way from the Sun to the end of the trail when she stopped to have a snack she had hiked 3 1/2 what is the distance in miles between the start and end of the trial
To find the distance between the start and end of the trail, we need to determine Rachel's position when she stopped for a snack.
Rachel had hiked 2/3 of the way from the Sun to the end of the trail before taking a break. Let's represent the distance from the Sun to the end of the trail as "x".
Since Rachel had hiked 2/3 of the way from the Sun to the end of the trail, we can calculate this distance by multiplying 2/3 by x:
(2/3) * x
Rachel had hiked 3 1/2 (3.5) miles when she stopped for a snack. So, we can also represent this distance as 3.5:
(2/3) * x = 3.5
To find the value of "x", we can solve this equation. We'll start by isolating the variable "x" on one side:
x = 3.5 / (2/3)
To divide by a fraction, we can multiply by its reciprocal:
x = 3.5 * (3/2)
Performing the multiplication:
x = 10.5 / 2
x = 5.25
Therefore, the distance between the start and end of the trail is 5.25 miles.
Let's assign a variable to the total distance between the start and end of the trail. Let's call it "x" miles.
According to the information provided, Rachel had hiked 2/3 of the way from the Sun to the end of the trail when she stopped to have a snack. This means that she had hiked 2/3 of the total distance, or (2/3)x miles.
After having a snack, she hiked an additional 3 1/2 miles. We can represent this as 3 1/2, which is equal to 7/2 in improper fraction form.
Therefore, the total distance traveled by Rachel can be represented by the equation:
(2/3)x + 7/2 = x
To solve for "x", we need to find a common denominator for the fractions and then solve for "x".
Multiplying both sides of the equation by 6 (the least common multiple of 3 and 2) gives us:
2(2x) + 7(3) = 6x
4x + 21 = 6x
Subtracting 4x from both sides of the equation, we get:
21 = 2x
Dividing both sides of the equation by 2 gives us:
x = 10.5
Therefore, the distance between the start and end of the trail is 10.5 miles.
To find the distance between the start and end of the trail, we need to calculate the total distance Rachel hiked before she stopped for a snack.
Let's assume the total distance from the start to the end of the trail is represented by the variable "x" (in miles).
Rachel had already hiked 2/3 of the way from the Sun to the end of the trail before stopping for a snack. This means she hiked (2/3)x miles.
After her snack, Rachel hiked an additional 3 1/2 miles.
So the total distance Rachel hiked would be (2/3)x + 3 1/2 miles.
To find the value of "x" in miles, we can set up an equation:
(2/3)x + 3 1/2 = x
To get rid of the fraction, let's convert 3 1/2 to an improper fraction:
3 1/2 = 7/2
Now our equation becomes:
(2/3)x + 7/2 = x
To solve for "x," let's isolate the "x" term on one side of the equation:
(2/3)x - x = -7/2
Multiplying both sides of the equation by 6 to eliminate the fractions:
2(2x) - 6x = -21
4x - 6x = -21
-2x = -21
Dividing both sides of the equation by -2:
x = (-21) / (-2)
x = 10.5
So the distance between the start and end of the trail is 10.5 miles.