Answer: 45 mph
Work Shown:
H = home, C = campground

Each distance is in miles. Each rate is in miles per hour (mph). Each time value is in hours.
The formula we need is: distance = rate*time
It shortens to d = r*t
Going from H to C, we have the equation d = r*4 or d = 4r
Then from C to H, we have the equation d = 3(r+15)
Both equations involve the same distance d because you traveled the same route both ways.
This means we can equate the right hand sides to solve for variable r.
4r = 3(r+15)
4r = 3r+45
4r-3r = 45
r = 45 mph is the final answer
The portion going from H to C you travel 45 mph. Going for 4 hours means the distance traveled was d = r*t = 45*4 = 180 miles.
Getting back home increases the speed to 45+15 = 60 mph. Then notice how time = distance/rate = 180/60 = 3 hours, which helps us see that you arrive back home 1 hour faster compared to when going from H to C. This helps confirm the answer is correct.