Question 21642
What you need to know is that the time it takes to travel over a distance is given by {{{distance / speed = time}}}.
This problem has three distances that are given as a shorter distance, a longer distance that is the short distance plus 96, and the total distance which (of course) is their sum.
Let x be the shorter distance. The time it took to travel over x was {{{x / 60}}}. The time it took to travel over x + 96 was {{{ (x + 96) / 120}}}. The time it took to travel over the entire distance was {{{ (x + x + 96) / 100}}}.
Of course, the time for the total distance must equal the sum of the times for each segment, so 
{{{(x / 60) + ((x + 96) / 120) = (2x + 96) / 100}}}
You solve this for x.
{{{(2x / 120) + ((x+96)/120) = (2x+96)/100}}} [get common denominator]
{{{(3x+96)/120 = (2x+96)/100}}} [simplify]
{{{300x +(100)*(96)=240x +(120)*(96)}}} [multiply both sides by both denominators]
{{{60x = (20)*(96)}}} [simplify]
{{{3x = 96}}} [divide both sides by 20]
{{{x=32}}} [divide both sides by 3]
So, x+96= 128, and the total distance is 160.
Check by calculating the time taken for each segment and for the total:
32/60 = .5333333333...
128/120 = 1.06666666...
160/100 = 1.6
.5333333... + 1.06666666... = 1.6 [think of it as .5 and 1/3 of a tenth plus 1.0 and 2/3 of a tenth, which is 1.5 plus a whole tenth]