Solve this multi-step problem. A runner completes 1/4 of a 5-mile race every 8 minutes. At the same pace, how far can the runner go in 16 minutes?(1 point) Responses 110 mile Start Fraction 1 over 10
To find out how far the runner can go in 16 minutes, we need to determine the fraction of the race the runner completes in 16 minutes.
The runner completes 1/4 of the race every 8 minutes. In 16 minutes, the runner would complete 2 sets of 1/4 of the race.
2 sets of 1/4 of the race is equivalent to 2 * 1/4 = 2/4 or 1/2 of the race.
Since the race is 5 miles, the runner can go 1/2 * 5 = 2.5 miles in 16 minutes.
Therefore, the runner can go 2.5 miles in 16 minutes.
To solve this problem, we can set up a proportion to find the distance the runner can go in 16 minutes.
Step 1: Determine the proportion. Let x represent the distance the runner can go in 16 minutes.
1/4 mile is completed in 8 minutes.
Therefore, 1 mile is completed in 8 minutes × 4 = 32 minutes.
So, the proportion is: 1 mile / 32 minutes = x miles / 16 minutes.
Step 2: Cross-multiply and solve for x.
32 minutes * x miles / 16 minutes = 1 mile.
32x = 16.
Divide both sides by 32: x = 16/32 = 1/2 mile.
Therefore, the runner can go 1/2 mile in 16 minutes.
To solve this multi-step problem, we need to determine the distance the runner can cover in 16 minutes at the same pace of completing 1/4 of a 5-mile race every 8 minutes.
First, we need to find out how many sets of 8 minutes are in 16 minutes. By dividing 16 by 8, we get 2 sets of 8 minutes.
Since the runner completes 1/4 of a 5-mile race every 8 minutes, we can calculate how much distance the runner covers in one set of 8 minutes. To do this, we multiply 1/4 by 5 miles:
(1/4) * 5 = 5/4 miles
Now we know that in one set of 8 minutes, the runner covers 5/4 miles. Since there are 2 sets of 8 minutes in 16 minutes, we can multiply 5/4 by 2 to find the total distance covered in 16 minutes:
(5/4) * 2 = 10/4 miles
Simplifying the fraction, we get:
10/4 = 2.5 miles
Therefore, the runner can go 2.5 miles in 16 minutes at the same pace.