SOLUTION: Marie rode her bicycle from her home to the bicycle shop in town and then walked back home. If she averaged 6 miles per hour riding and 3 miles per hour walking, how far is it from

Question 110248: Marie rode her bicycle from her home to the bicycle shop in town and then walked back home. If she averaged 6 miles per hour riding and 3 miles per hour walking, how far is it from her home to the bicylce shop if her total travel was 1 hour?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The basic formula for this sort of problem is .
:
In this problem, you have two calculations of rate times time that equal the same distance since the distance going to the bicycle shop is the same as the distance for the return trip. What we have to deal with first is the fact that there are two different travel times, let's call the time going to the shop as t1, and the return time t2.
:
So the distance to the shop is 6 miles per hour times t1 hours,

and the return trip distance is:

and we can say that

:
We also know that , because the total travel time was 1 hour.
:
Putting that second fact another way, namely: and then substituting in the first equation:
:

:
Now we know that it took Marie 2/3 hour to walk home at 3 miles per hour.
:
Using , , so the distance from home to the shop is 2 miles.
:
Check:
Walk home takes 2/3 hour, so the bike ride took 1/3 hour.

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