The roadrunner leaves Pittsburgh at 7:15 in the morning at 10mph. He is headed toward Cleveland which is 131 miles away. If the coyote leaves 15 minutes later, what speed will he have to travel to get there at the same time as the road runner?

To find out what speed the coyote needs to travel to reach Cleveland at the same time as the roadrunner, we need to determine the time it will take for both of them to reach Cleveland.

First, let's calculate the roadrunner's travel time. We know that distance = speed × time. The distance between Pittsburgh and Cleveland is 131 miles and the roadrunner's speed is 10 mph. So, the roadrunner's travel time is:

time = distance / speed = 131 miles / 10 mph = 13.1 hours

Now, let's consider the coyote. We know that the coyote leaves 15 minutes (or 0.25 hours) after the roadrunner. Therefore, the coyote has slightly less time to cover the same distance.

Let's denote the coyote's speed as v mph. Since both the roadrunner and the coyote are traveling the same distance, we can set up the equation:

roadrunner's time = coyote's time

13.1 hours = (131 miles / 10 mph) + (131 miles / v mph)

Simplifying this equation gives us:

13.1 hours = 13.1 hours + (131 miles / v mph)

Now, we can subtract 13.1 hours from both sides of the equation:

(131 miles / v mph) = 0

Since the coyote needs to cover the 131-mile distance in 0 hours, this means the coyote needs to travel at an infinitely fast speed, which is not physically possible.

Therefore, if the coyote leaves 15 minutes later, it is not possible for it to reach Cleveland at the same time as the roadrunner, regardless of its speed.