Question

An athlete knows that when she jogs along her neighborhood​ greenway, she can complete the route in 14 minutes. It takes 42 minutes to cover the same distance when she walks. If her jogging rate is 4 mph faster than her walking​ rate, find the speed at which she jogs.

Answer 1

Let's assume that the distance covered by the athlete is d, and her walking speed is w.

According to the problem, the time it takes for the athlete to complete the route when she jogs is 14 minutes, which can be expressed as:

d / (w + 4) = 14/60 (converting minutes to hours)

Simplifying this equation, we get:

d = 14/60 * (w + 4)

Similarly, the time it takes for her to complete the same route when she walks is 42 minutes, or:

d / w = 42/60

Simplifying this equation, we get:

d = 42/60 * w

Since both expressions for d are equal, we can set them equal to each other and solve for w:

14/60 * (w + 4) = 42/60 * w

Multiplying both sides by 60 to get rid of the denominators, we get:

14(w + 4) = 42w

Expanding and simplifying, we get:

14w + 56 = 42w

Subtracting 14w from both sides, we get:

56 = 28w

Dividing both sides by 28, we get:

w = 2

So the athlete's walking speed is 2 mph. We can use this to find her jogging speed:

jogging speed = walking speed + 4

jogging speed = 2 + 4

jogging speed = 6 mph

Therefore, the athlete jogs at a speed of 6 mph.