To train for the running of a triathlon, Jerri jogs 1 hour each day over the same 7-mile course. Four miles of the course is downhill, whereas the other 3 miles is on level ground. Jerri figures that she runs 2 miles per hour faster downhill than she runs on level ground. Find the rate at which Jerri runs on level ground.

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