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Jack’s car started from point P toward point Q. At the same time, Jill’s car started at point Q toward point P. They crossed paths (assume there were no crashes) at point R. They continued on their paths, with Jack’s car reaching point Q nine hours after they had crossed paths. Jill’s car reached point P four hours after they had crossed paths. Both cars maintained a constant speed through the journey. Jack’s car maintained 36 mph. What was the speed of Jill’s car, in mph?

 Feb 23, 2020
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P       R          Q

               324      

 

Note  that if it took  Jack 9 hrs  to go from R  to Q....then the distance  from Q to R must  be  9 * 36  = 324 miles

 

So.....let T  be  the time it takes both to reach  R

 

So....Jills Rate  (in mph)  must   be  : 

[Distance from Q ot R] / [Time to  travel from Q to R] =   324 / T

 

So....the  distance that Jack travels  must  be  36T  + 324

 

And  the distance that Jill travels  must be  324  +  her rate *  time to  travel  from R to P  =

 324  + (324/ T)  *  4

 

Since  these distances are the same, we have this equation :

 

36T  + 324   =  324  + (324/ T)  *  4          subtract   324  from both sides

 

36T =  ( 324/T ) * 4

 

36T  = 1296 /T      multiply both sides  by  T

 

36T^2   =1296       divide both sides by  36

 

T^2  =36    take the square root of both sides

 

T = 6  hrs

 

So  Jill's rate must be      324 /  6   = 54 mph

 

 

cool cool cool

 Feb 23, 2020

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