Final answer:
It will take 3 hours for the boys to be 9 miles apart.
Step-by-step explanation:
To find the number of hours it will take for the boys to be 9 miles apart, we can set up an equation using the formula:
Distance = Speed × Time.
Let's assume the time it takes for the boys to be 9 miles apart is 't' hours.
For the boy cycling at 15 miles per hour, the distance covered in 't' hours is 15t miles.
For the boy cycling at 12 miles per hour, the distance covered in 't' hours is 12t miles.
Since they are cycling in the same direction, the distance between them will be the difference between the distances they covered:
15t - 12t = 9 miles
Simplifying the equation, we get:
3t = 9
Dividing both sides of the equation by 3, we find that 't' is equal to 3.
So, it will take 3 hours for the boys to be 9 miles apart.