Susan and Katie are running an ultra marathon. Susan averages 5 miles per hour. Katie averages 5.2 miles per hour. If Susan gets a 45 minute head start, then exactly how many hours after Katie begins
running will she catch up to Susan?

Katie will catch up to Susan after running 33.4 h.

Step-by-step explanation:

We can find the time that takes Katie to catch up to Susan by using the following equation:

Where:        

: is the final position of Katie

: is the initial position of Katie = 0

: is the initial speed of Katie = 5.2 mi/h

a: is the acceleration = 0 (she is moving at constant speed)

t: is the time

Since Katie will catch up to Susan, the final distance traveled by Katie will be equal to the final distance traveled by Susan.

Since Susan gets a 45 minutes head start, in that time she traveled the following distance:      

So, this will be the initial position of Susan.

Hence, the time will be:

Therefore, Katie will catch up to Susan after running 33.4 h.

I hope it helps you!            

351.23

step-by-step explanation:

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