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?
1/8 miles
1/10 miles
160 miles
2 1/2 miles
To find out how far the runner can go in 16 minutes, we can set up a proportion.
Since the runner completes 1/4 of a 5-mile race every 8 minutes, we can say that in 8 minutes, the runner can run 1/4 of a mile.
We can set up the proportion as:
8 minutes / 1/4 mile = 16 minutes / x miles
To solve for x, we can cross multiply:
8 * x = 16 * 1/4
8x = 4
Dividing both sides by 8:
x = 1/2
Therefore, the runner can go 1/2 mile in 16 minutes.
Answer: 1/2 miles
wrong
I apologize for the mistake. Let's correct the solution.
The runner completes 1/4 of a 5-mile race every 8 minutes, so in 1 minute, the runner can complete 1/4 divided by 8 = 1/32 of a mile.
To find out how far the runner can go in 16 minutes, we can multiply the distance completed in 1 minute by the number of minutes:
(1/32) mile/minute * 16 minutes = 16/32 = 1/2 mile.
Therefore, the runner can go 1/2 mile in 16 minutes.
Answer: 1/2 miles
2 1/2 miles
I apologize for the previous incorrect response. Let's solve the problem correctly this time.
If the runner completes 1/4 of a 5-mile race every 8 minutes, then in 1 minute, the runner can complete 1/4 divided by 8, which is 1/32 of a mile.
To find out how far the runner can go in 16 minutes, we can multiply the distance completed in 1 minute by the number of minutes:
(1/32) mile/minute * 16 minutes = 16/32 = 1/2 mile.
Therefore, the runner can go 1/2 mile in 16 minutes. However, this is not the correct answer. I apologize for the confusion in my response.
Since the runner's pace remains the same, the runner can complete 1/4 of the race every 8 minutes. So in 16 minutes, the runner can complete 1/4 + 1/4 = 2/4 = 1/2 of the race.
Since the total race is 5 miles, the runner can go (1/2) * 5 = 5/2 = 2 1/2 miles in 16 minutes.
Therefore, the correct answer is 2 1/2 miles.
I apologize for any confusion caused by the previous incorrect responses.
To solve this problem, we need to figure out how many 1/4-mile intervals the runner can complete in 16 minutes.
1/4 of a 5-mile race is (1/4) x 5 = 5/4 = 1.25 miles.
The runner completes 1.25 miles every 8 minutes.
To find out how many 1/4-mile intervals the runner completes in 16 minutes, we need to divide 16 by 8:
16 ÷ 8 = 2
So, in 16 minutes, the runner can complete 2 intervals of 1.25 miles each.
Therefore, the runner can go 2 x 1.25 = 2.5 miles in 16 minutes.
The answer is 2 1/2 miles.
To solve this problem, we can use the given information about the runner's pace.
We know that the runner completes 1/4 of a 5-mile race every 8 minutes. This means that in 8 minutes, the runner covers 1/4 of 5 miles.
To find out how far the runner can go in 16 minutes, we need to double the time (since 16 minutes is twice 8 minutes) and also find out how much distance the runner covers in that time.
To find the distance for 16 minutes, we can set up a proportion:
8 minutes --> 1/4 mile
16 minutes --> x (unknown distance)
We can solve this proportion by cross-multiplication:
8 × x = 16 × 1/4
8x = 4
Now, we can solve for x by dividing both sides of the equation by 8:
x = 4/8
Simplifying the fraction gives us:
x = 1/2
Therefore, the runner can cover 1/2 mile in 16 minutes at the same pace.
So, the correct answer is: 1/2 mile.