SOLUTION: James and pat are driving from Atlanta to Jacksonville a distance of 130 miles. james whos average rate is 5 mph faster than pats will drive first and then pat will drive the rest

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Question 1057674: James and pat are driving from Atlanta to Jacksonville a distance of 130 miles. james whos average rate is 5 mph faster than pats will drive first and then pat will drive the rest of the way. If the total driving time is 5 hours determine the average rate of each driver
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!
Uniform Travel Rate Rule is RT=D. 
              RATE      TIME      DISTANCE
JAMES         r+5
PAT           r
Total                    5          130

Two unknown variables are needed; or maybe just one? 


              RATE      TIME      DISTANCE
JAMES         r+5        j        (r+5)j
PAT           r          p         rp
Total                    5          130

Three variables but only two equations:

Mostly infinite results possible for r.
Answer by ikleyn(52887)   (Show Source): You can put this solution on YOUR website!
.
James and Pat are driving from Atlanta to Jacksonville a distance of 130 miles. James whos average rate is 5 mph faster
than Pat's will drive first and then Pat will drive the rest of the way.
If the total driving time is 5 hours determine the average rate of each driver
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Under the given conditions, the problem has more than one solution.
More precisely, it has INFINITELY many solutions. 

For example, these two sets are the solutions:


1.  James drives 2 hours at the rate 23 mph, and then Pat drives 3 hours at the rate 28 mph.   

    // 2*23 + 3*28 = 130 and all other conditions are satisfied.



2.  James drives 3 hours at the rate 24 mph, and then Pat drives 2 hours at the rate 29 mph.   

    // 3*24 + 2*29 = 130 and all other conditions are satisfied.


Actually, the problem requires to impose more restrictions (at least one more restriction) in order for the solution be unique.


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