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 as a fraction
Let's break down the problem step-by-step:
Step 1: Rachel had hiked 2/3 of the way from the Sun to the end of the trail.
Step 2: Rachel hiked 3 1/2 (which is equal to 7/2) from where she stopped to have a snack.
Step 3: To find the total distance of the trail, we need to calculate the distance from the Sun to where Rachel stopped and add it to the distance she hiked after the snack.
Distance from the Sun to where Rachel stopped:
= 2/3 of the total distance of the trail
Distance Rachel hiked after the snack:
= 7/2
Step 4: We need to add the two distances to find the total distance of the trail:
Total distance of the trail = Distance from the Sun to the snack spot + Distance hiked after the snack
Total distance of the trail = (2/3) + (7/2) = (4/6) + (21/6) = (25/6)
Therefore, the distance between the start and end of the trail, as a fraction, is 25/6.
Let's assume the distance between the start and end of the trail is represented by the variable "x."
According to the given information, 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 she had hiked 2/3 * x = 2x/3 miles.
After having a snack, Rachel hiked 3 1/2 more miles. This can be written as 3 + 1/2 = 7/2 miles.
Therefore, the total distance Rachel hiked is 2x/3 + 7/2 miles.
Since this distance is equal to the length of the entire trail, we can write the equation:
2x/3 + 7/2 = x
To solve for x, we can multiply both sides of the equation by 6 to eliminate the fractions:
2(2x) + 3(7) = 6x
4x + 21 = 6x
Subtracting 4x from both sides:
21 = 2x
Dividing both sides by 2:
x = 21/2
Therefore, the distance between the start and end of the trail, represented by the fraction, is 21/2.
To find the distance between the start and end of the trail as a fraction, let's break down the given information.
It is mentioned that Rachel had hiked 3 1/2 of the way from the Sun to the end of the trail when she stopped for a snack. Let's represent the distance from the Sun to the end of the trail as "x." According to the information given, Rachel had hiked 2/3 of the way from the Sun to the end of the trail when she stopped. We can represent this as (2/3)x.
Given that Rachel hiked 3 1/2 of the distance from the Sun to the end of the trail, we can write the following equation:
(2/3)x = 3 1/2
To solve this equation, first, convert the mixed number 3 1/2 to an improper fraction:
3 1/2 = (2 * 3) + 1/2 = 7/2
Now, rewrite the equation:
(2/3)x = 7/2
To isolate x, multiply both sides of the equation by the reciprocal of (2/3), which is (3/2):
x = (7/2) * (3/2)
Multiply the numerators and denominators:
x = 21/4
So, the distance between the start and end of the trail, represented as a fraction, is 21/4.