Solve this multi step problem. A runner compleats 1/4 of a 5 mile race every 8 minutes. At the same pace , how far can the runner go in 16 minutes?
First, we need to find the distance the runner covers in 1 minute.
Since the runner completes 1/4 of a 5-mile race every 8 minutes, it means the runner completes 1 mile every 8 minutes.
So, the runner covers 1 mile in 8 minutes.
Therefore, the runner covers 1/8 mile in 1 minute.
Now we can find the distance the runner can go in 16 minutes.
In 16 minutes, the runner covers 1/8 mile per minute.
So, in 16 minutes, the runner covers 1/8 mile/minute * 16 minutes = 2 miles.
Therefore, the runner can go 2 miles in 16 minutes.
To find out how far the runner can go in 16 minutes at the same pace, we need to determine how much distance the runner covers in 1 minute first.
Step 1: Calculate the distance covered 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 1/4 (distance covered in 8 minutes) by 8 (minutes).
1/4 ÷ 8 = 1/32
Step 2: Calculate the distance covered in 16 minutes
Now that we know the runner covers 1/32 of a mile in 1 minute, we can determine the distance covered in 16 minutes by multiplying 1/32 (distance covered in 1 minute) by 16 (minutes).
1/32 × 16 = 1/2
Therefore, at the same pace, the runner can go 1/2 mile in 16 minutes.
To solve this multi-step problem, we need to first determine the runner's speed (in miles per minute) and then use that speed to calculate how far the runner can go in 16 minutes.
Step 1: Calculate the runner's speed (in miles per minute)
Given that the runner completes 1/4 of a 5-mile race in 8 minutes, we can set up a proportion to find the runner's speed.
Let x represent the runner's speed (in miles per minute).
1/4 = x/8
To find x, we can cross-multiply:
1 * 8 = 4 * x
8 = 4x
Now, divide both sides by 4 to solve for x:
8/4 = x
2 = x
Therefore, the runner's speed is 2 miles per minute.
Step 2: Calculate how far the runner can go in 16 minutes
Now that we know the runner's speed (2 miles per minute), we can use this information to determine how far the runner can go in 16 minutes.
Let d represent the distance the runner can go in 16 minutes.
We can set up a proportion using the runner's speed:
2 miles/1 minute = d miles/16 minutes
To find d, we can cross-multiply:
2 * 16 = 1 * d
32 = d
Therefore, the runner can go 32 miles in 16 minutes.
So, the answer to the problem is that at the same pace, the runner can go 32 miles in 16 minutes.