Question 879591
The 2nd sentence was unclear to me so I changed it to what I thought you meant.
:
A motorist traveled from Town A to Town B.
 After traveling 1/3 of the distance at an average speed of 45 km/h, he continued to travel another 480 km to reach Town B.
 If his average speed for the entire journey was 54 km/h, what was his average speed for the last 2/3 of the distance?
:
From the information given, find the total distance (d) from  A to B
{{{2/3}}}d = 480
2d = 480 * 3
2d = 1440
d = 720 km
:
Find 1/3 of the total 
{{{1/3}}} * 720 = 240 km
:
Let a = ave speed for the last 2/3 of the journey
:
write a time equation, time = dist/speed
{{{240/45}}} + {{{480/a}}} = {{{720/54}}}
multiply by Least common multiple, 270a
270a*{{{240/45}}} + 270a*{{{480/a}}} = 270a*{{{720/54}}}
cancel the denomintors
6a(240) + 270(480) = 5a(720)
1440a + 129600 = 3600a
129600 = 3600a - 1440a
129600 = 2160a
a = 129600/2160
a = 60 km/hr for last 2/3 of the journey
:
:
Check this, find the times
240/45 = 5.33 hrs
480/60 = 8.00 hrs
--------------
total: = 13.33 hrs
and 
720/54 = 13.33 hrs