Math, I need help and would really appreciate it. I’m stuck.

Question

A jogger begins her workout by jogging to the park, a distance of 7 miles. She then jogs home at the same speed, but along a different route. This return trip is 14 miles, and her time is one hour longer. Find her jogging speed. Let x = the jogging speed.

Answer 1

distance=rate*time

d=r*t (r will represent the jogging speed, not x)

7=r*t

14=r(t+1)

from 7=rt, we get 7/r=t

substitute

14=r([7/r]+1)

14=7+r

r=14-7

r=7 mph is the jogging speed

also, t=1 hour for the 7 mile jog and it takes 2 hours for the 14 mile jog

Answer 2

Thought of a different way (using logic instead of algebra) (not worse or better, just different):

Going out on the trip was 7 miles.

The return trip, at the same speed, was 14 miles (twice as long)

To go twice as long, she ran an extra hour

Therefore, if doubling her trip meant adding another hour, the first part was also 1 hour.

7 miles in 1 hour = 7 mph