<PRE><B>Question 171770</B>
The rail line between two cities consists of two segments, one 96 km longer
 than the other. A passenger train averages 60 km/h over the shorter segment,
 120 km/h over the longer, and 100 km/h for the entire trip.
 How far apart are the cities?
:
Let d = distance of the shorter segment (traveled at 60 km/hr)
and
(d+96) = distance of the longer segment (traveled at 120 km/hr)
then 
2d + 96 = total distance between the two cities (average of 100 km/hr)
:
How about writing a time equation? Time = dist/speed:
:
{{{d/60}}} + {{{((d+96))/120}}} = {{{((2d+96))/100}}}
:
Multiply equation by 600 to get rid of the denominators; results:
10d + 5(d+96) = 6(2d+96)
:
10d + 5d + 480 = 12d + 576
:
10d + 5d - 12d = 576 - 480
:
3d = 96
d = {{{96/3}}}
d = 32 km the shorter segment
and
32 + 96 = 128 km the longer segment
then
2(32) + 96 = 160 km the total distance
:
:
Check solution by finding the times
32/60 + 128/120 = 160/100
.5333 + 1.0667 = 1.6
:
:
Did this make sense to you?</PRE>