It takes Marty 1 1/4 hours to get ready for school. If 1/5 of that time is used to take a shower and 1/3 of the time is used to
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If there is some scalar function 
such that
then we want to find
such that
So the vector field
is conservative, which means the fundamental theorem applies; the line integral of 
along any path 
parameterized by some vector-valued function 
over 
is given by
In this case,
then we want to find
So the vector field
In this case,