To train for the running of a triathlon, Jerri jogs 1 hour each day over the same 8-mile course. Six miles of the course is downhill, whereas the other 2 miles is on level ground. Jerri figures that she runs 3 miles per hour faster downhill than she runs on level ground. Find the rate at which Jerri runs on level ground.
A) 7 mph
B) 21 mph
C) 6 mph
D) 18 mph
E) 5 mph

Question

Quizplus · Accepted Answer

Let's call the rate at which Jerri runs on level ground "x". Then, her rate downhill would be "x+3" (since she runs 3 mph faster downhill).

We know that Jerri jogs the entire 8-mile course in 1 hour, so we can set up an equation:

6/(x+3) + 2/x = 1

This equation represents the fact that it takes Jerri 6/(x+3) hours to jog the 6 miles downhill, and 2/x hours to jog the 2 miles on level ground. Adding those times together should give us a total time of 1 hour.

Now we just need to solve for x:

6/(x+3) + 2/x = 1

Multiplying both sides by (x)(x+3) gives us:

6x + 18 + 2(x+3) = x(x+3)

Expanding and simplifying:

8x + 24 = x^2 + 3x

Putting everything on one side:

x^2 - 5x - 24 = 0

Factoring:

(x-8)(x+3) = 0

So x could either be 8 or -3. Since we're looking for a rate that makes sense in the context of the problem, we can eliminate the negative solution. Therefore, Jerri runs on level ground at a rate of 8 mph.

To Train for the Running of a Triathlon, Jerri Jogs