Question

Lorena walks the path around the park in 30 minutes. If she jogs, it takes her 20 minutes. Her jogging speed is 2 miles per hour faster than her walking speed. Find Lorena’s walking speed and jogging speed.

Answer 1

rate x time = distance

the distances are equal

x(30) = (x + 2)(20)
30x = 20x + 40
10x = 40
x = 4 mph
x + 2 = 6 mph
The distance is 2 miles

Answer 2

walking speed= 4mph jogging speed =6 mph

Explanation:

We are asked to find Lorena’s walking speed and jogging speed. Let’s let r represent Lorena’s walking speed in miles per hour and t represent time in hours. In 30min=1/2hr, she walks a distance rt=r/2 miles. Since her jogging speed is 2 miles per hour faster, we represent that as r+2. In 20min=1/3hr, she jogs a distance (r+2) t=r+2/3 miles. We can set these expressions for the distance around the park equal to find

r/2 = r+2/3

Multiplying both sides by 6 and then subtracting 2r from both sides yields

6 (r/2) = 6 (r+2/3)

3r = 2r +4

3r−2r = 2r + 4 -2r

r = 4

Thus, Lorena’s walking speed is r = 4 miles per hour and her jogging speed is r+2=6 miles per hour.