# Homework Help: Simple Uniform Motion Problem

1. Oct 21, 2015

1. The problem statement, all variables and given/known data
Marlene rides her bicycle to her friend Jon's house and returns home by the same route. Marlene rides her bike at constant speeds of 6 mph on level ground, 4 mph when going uphill, and 12 mph when going downhill. If her total time riding was 1 hour, how far is it to Jon’s house?

2. Relevant equations
d=rt
t=d/r

3. The attempt at a solution

t1+t2+t3=1hour

L/6mph+U/4mph+D/12mph=1hour

I have tried solving for each variable independently and then substituting it, but when I do that all my terms cancel out and I am either left with 1=1 or 12=12 depending of which equation I start with.

I understand that Marlene traveled different distances at different rates, and for different intervals of time. I know that the total distance traveled in 1 hour must be 6 miles but I can't seem to express it mathematically.

2. Oct 21, 2015

### SteamKing

Staff Emeritus
If Marlene travels a certain distance uphill on her way to Jon's house, does she travel this same distance uphill on her way back home?

3. Oct 21, 2015