<PRE><B>Question 15678</B>
Let x = rate going (for 3 hours) 
x+8 = rate returning (faster) (for 2 hours)


D=RT
 (RT going) + (RT returning) = Total Distance
3x + 2(x+8) = 291
3x + 2x + 16 = 291
5x = 275
x= 55 mph going
x+8 = 63 mph returning


Check:  See if total distance = 291 miles
3(55) + 2(63) = 291
165 + 126 = 291


However, there is a problem here.  Notice that the distance going is 165 miles and the return trip was only 126 miles.  What happened??  Did the consultant find a shortcut to come home??  We would normally assume that the distance going and coming would be the same. However, that would give a completely different problem in which 


D going = D returning
RT (going) = RT returning
3x = 2(x+8) 
3x = 2x + 16
x=16 mph going
x+8 = 24 mph returning


However this does NOT give you a total trip of 291 miles.  I think there is a problem (an oversight!) in this problem.


R^2 at SCC</PRE>