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.