Solving Simple Uniform Motion Problem: Marlene's Bicycle Ride to Jon's House

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Marlene rides her bicycle to Jon's house and back, traveling at different speeds: 6 mph on level ground, 4 mph uphill, and 12 mph downhill, with a total riding time of 1 hour. The problem requires calculating the distance to Jon's house, which is determined to be 3 miles. The equations d=rt and t=d/r are used to express the relationship between distance, rate, and time. The challenge arises in accurately representing the varying distances and speeds mathematically, leading to confusion when attempting to isolate variables. Ultimately, it is confirmed that Marlene travels the same distance uphill on her return trip downhill.
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Homework Statement


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?

Answer = 3 miles

Homework Equations


d=rt
t=d/r

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. [/B]
 
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ADMO said:

Homework Statement


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?

Answer = 3 miles

Homework Equations


d=rt
t=d/r

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. [/B]
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?
 
SteamKing said:
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?
She would travel the same distance, but she will be going downhill where ever she initially traveled uphill.
 

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