A backpacking team is hiking At an average speed of 2 1/2 miles per hour. At that rate, how long will it take for a hike of 8 3/4 mi?

Let's convert these fractions to decimals.

2 1/2 = 2.5
8 3/4 = 8.75

Set up a proportion. Cross multiply and solve for x.

2.5/1 = 8.75/x

To calculate the time it will take for the backpacking team to hike a distance of 8 3/4 miles at an average speed of 2 1/2 miles per hour, we can use the formula:

Time = Distance / Speed

First, let's convert the mixed number 2 1/2 to an improper fraction:

2 1/2 = 5/2

Now let's substitute the values into the formula:

Time = 8 3/4 / 5/2

Next, let's convert the mixed number 8 3/4 to an improper fraction:

8 3/4 = 35/4

Now let's calculate the time:

Time = 35/4 / 5/2

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

Time = 35/4 * 2/5

Now let's simplify the fractions:

Time = (35 * 2) / (4 * 5)

Time = 70 / 20

Time = 7/2

Therefore, it will take the backpacking team 7/2 hours to hike a distance of 8 3/4 miles at an average speed of 2 1/2 miles per hour.

To calculate the time it will take for the backpacking team to complete a hike of 8 3/4 miles at an average speed of 2 1/2 miles per hour, we need to divide the distance by the speed.

Step 1: Convert the mixed number to an improper fraction.
2 1/2 is equal to (5/2) in improper fraction form.

Step 2: Divide the distance by the speed.
To find the time, we divide the distance (8 3/4 miles) by the speed (2 1/2 miles per hour):

(35/4) ÷ (5/2)

Step 3: Simplify the division.
When dividing by a fraction, we multiply by its reciprocal. Therefore, we multiply by (2/5):

(35/4) × (2/5)

Step 4: Simplify the multiplication.
Multiply the numerators and multiply the denominators:

(35 × 2) / (4 × 5)
= 70/20

Step 5: Simplify the fraction.
To simplify the fraction, divide the numerator and denominator by their greatest common divisor, which is 10:

(70 ÷ 10) / (20 ÷ 10)
= 7/2

Step 6: Convert the improper fraction to a mixed number.
7/2 can be written as the mixed number 3 1/2.

Therefore, it will take the backpacking team 3 1/2 hours to complete a hike of 8 3/4 miles at an average speed of 2 1/2 miles per hour.