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.

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

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