Question 66510
The average speded for 36 miles = 12mph
Time taken = distance/time
           = 36/12
           = 3 hrs

The average speed for next 45 miles = 15 mph
Time taken = distance/time
           = 45/15
           = 3 hrs

Let the speed for the next 54 miles = x mph
time taken = distance/speed
           = 54/x

Total distance = 36 + 45 + 54
               = 135 miles

Total time = 3 + 3 + 54/x
           = 6 + 54/x
           = (6x + 54)/x hrs  [taking LCM and adding]

THus the average speed for the entire journey = distance /time

                                              = 135/ (6x+54)/x
                                             = 135x/(6x+54)

Given the overall speed = 15 mph

==>  135x/(6x+54)  = 15
==> 135x = 15(6x+54)
==> 135x = 90x + 810
==> 135x - 90x = 810
==> 45x = 810
==> x = 810/45
==> x = 18

Thus the speed for the last 54 miles has to be 18 mph to get an overall average speed of 15 mph


Good Luck!!!