Answer: the rate at which Jerri runs on level ground is 6 mph
Step-by-step explanation:
Let x represent the rate at which Jerri runs on level ground.
Jerri figures that she runs 2 miles per hour faster downhill than she runs on level ground. This means that the speed at which she runs downhill is (x + 2) mph
Time = distance/ speed
Four miles of the course is downhill. This means that the time it takes her to run downhill is
4/(x + 2)
Whereas the other 3 miles is on level ground. This means that the time it takes her to run on level ground is
3/x
Jerri jogs 1 hour each day over the same 7-mile course. This means that
4/(x + 2) + 3/x = 1
Cross multiplying by x(x + 2), it becomes
4x + 3(x + 2) = x(x + 2)
4x + 3x + 6 = x² + 2x
x² + 2x - 4x - 3x - 6 = 0
x² - 5x - 6 = 0
x² + x - 6x - 6 = 0
x(x + 1) - 6(x + 1) = 0
x - 6 = 0 or x + 1 = 0
x = 6 or x = - 1
Since the speed cannot be negative, then x = 6 mph
