Solve this multi-step problem. A runner completes a 1/4 of a 5-mile race every 8 minutes. at the same pace how far can the runner go in 16 minutes
To solve this problem, we need to determine the distance the runner can go in 16 minutes by finding the proportion using the given information.
The runner completes 1/4 of a 5-mile race every 8 minutes. This means in 8 minutes, the runner can cover 1/4 of the race, which is 5/4 mile.
To find how far the runner can go in 16 minutes, we need to calculate the distance covered in 8 minutes and then double it.
Distance covered in 8 minutes = 5/4 mile
Distance covered in 16 minutes = 2 * (5/4) = 10/4 = 5/2 mile
Therefore, the runner can go 5/2 mile in 16 minutes.
simplify
To simplify the expression 5/2, we can divide both the numerator and denominator by their greatest common divisor, which is 1.
So, simplifying 5/2 gives us the simplified fraction of 2 1/2 or 2.5 as a decimal.
can it be 2 1/2
Apologies for the confusion. Yes, you are correct. The simplified fraction 5/2 can also be expressed as a mixed number, 2 1/2. This represents 2 whole units and 1/2 unit.
To solve this multi-step problem, we need to find out how far the runner can go in 16 minutes, given that they complete 1/4 of a 5-mile race every 8 minutes.
Step 1: Determine the distance covered by the runner in 8 minutes
The runner completes 1/4 of a 5-mile race every 8 minutes. Therefore, in 8 minutes, the distance covered by the runner is:
1/4 * 5 miles = 5/4 miles
Step 2: Determine the distance covered by the runner in 16 minutes
Since the runner covers 5/4 miles in 8 minutes, we can use this as a ratio to find out how far they can go in 16 minutes. Set up a proportion:
8 minutes / 5/4 miles = 16 minutes / x miles
Step 3: Solve the proportion
To solve the proportion, we can cross multiply:
8 * x miles = 5/4 * 16 minutes
Step 4: Simplify the equation
Simplifying the equation, we get:
8x = 20
Step 5: Solve for x
Dividing both sides of the equation by 8:
x = 20 / 8
x = 2.5
Step 6: Answer
Therefore, in 16 minutes, the runner can go a distance of 2.5 miles.
To solve this problem, we can start by finding the distance the runner covers in 1 minute.
Since the runner completes 1/4 of a 5-mile race in 8 minutes, we can calculate the distance covered in 1 minute by dividing the distance covered in 8 minutes by 8.
Distance covered in 8 minutes = 1/4 * 5 miles = 5/4 miles
Distance covered in 1 minute = (5/4) miles / 8 = 5/32 miles
Now, we know the distance the runner covers in 1 minute is 5/32 miles. To find out how far the runner can go in 16 minutes, we multiply the distance covered in 1 minute by 16.
Distance covered in 16 minutes = (5/32) miles * 16 = 80/32 = 2.5 miles
Therefore, the runner can go 2.5 miles in 16 minutes.