Question 719003

BIG PROBLEM: SEE BELOW!


Deciding how to organize the data is what makes this problem more difficult than usual.  My solution is not the exactly typical R T D table.  


Instead of x AM or y PM, try counting time in hours starting from a 0 point.  8PM is t=0 and 11AM is t at 15.  We must also use rate*time=distance.


Car_________Rate_________Distance when time 15____________Distance time 15+t
Early fast___40__________{{{40*15}}}____________________________{{{40*15+40*t}}}
Late slow_____45_________0________________________________{{{45*t}}}
TOTAL DISTANCE____________________________________________{{{460}}}


Regardless of when either car leaves its starting point, they meet when the sum of distances is 460 miles, and the expressions to sum are now written and in the table.


This is the essential starting equation for the problem:
{{{highlight(40*15+40t+45t=460)}}}.  Solve for {{{t}}} and add this to the "11AM" time designation.


BIG PROBLEM: Instead of finding the equation just given as meaningful, it cannot be correct because the problem description is flawed.  The the 15 hour time that the fast early car drives and before or at the time the second car begins, the fast car will have gone 600 miles.  This is much farther than the distance between the two towns.  Are you SURE you did not maybe give wrong start times for these two cars?