Final answer:
To determine how long it would take to ride 15 miles at a steady speed, given that it takes 30 minutes to ride 6 miles, we set up a direct proportion. The calculation shows that it would take 75 minutes, which is a reasonable time.
Step-by-step explanation:
The question involves determining the time it takes to ride a bike a certain distance at a steady speed, which is a problem of setting up a direct proportion.
Since the cyclist rides 6 miles in 30 minutes, to find out how long it would take him to ride 15 miles, we can set up the proportion as follows:
(6 miles / 30 minutes) = (15 miles / x minutes)
To solve for x, we cross-multiply and get:
6x = 15 × 30
x = (15 × 30) / 6
x = 75 minutes
Therefore, it would take the cyclist 75 minutes to ride his bike 15 miles at the same steady speed.
It is always good to double-check if the answer is reasonable. If we know he rides 6 miles in 30 minutes, we would expect him to ride three times that distance, which is 18 miles, in 90 minutes. Since 15 miles is less than 18 miles, riding for 75 minutes seems reasonable.