If a man can run \( p \) miles in \( x \) minutes, how long will it take him to run \( q \) miles at the same rate?

If a man can run p miles in x minutes, we can find his running rate by dividing the distance by time. To maintain the same rate for a different distance, say, q miles , we can set up a proportion since the rate of speed remains constant. Let's call the unknown time t minutes . The proportion is:
p miles / x minutes = q miles / t minutes
We can solve for t by cross-multiplying and dividing:
t = (q miles * x minutes) / p miles
To answer the student's question concerning how long it will take the man to run q miles at the same rate, we use the above formula. For example, if he runs 3 miles in 30 minutes, and we want to know how long it takes him to run 6 miles, we'd have:
t = (6 miles * 30 minutes) / 3 miles
t = 60 minutes
The man would take 60 minutes to run 6 miles at the same pace.

Answered by Qwship | 2024-06-24

To find the time t to run q miles, use the formula t = p q ⋅ x ​ . For example, if he runs 3 miles in 30 minutes, then running 6 miles will take 60 minutes. This method uses proportions derived from his running rate to determine the time needed for a different distance.
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Answered by Qwship | 2024-12-23