Question 262158
This problem involves the use of the equation d=vt, where d = distance, v = velocity and t = time.

Let d = the distance between Chicago and LA
v = 640mph
t = time of flight

d=vt
{{{d=640*t}}}

On the return trip, the distance is the same, d, but it takes 48 minutes longer.

Convert 48 minutes to hours: 48/60 = 0.80 hours

the equation for the return trip is:

d = vt
d = (512)(t+0.8)

The two distances are the same (the original trip and the return trip) so we can just equate them:

d = d
{{{640*t = (512)(t+0.8)}}}
{{{640*t = 512*t + 512*0.8}}}


Minus 512t from both sides:

{{{128*t = 409.6}}}


Divide both sides by 128:

{{{ t = 409.6/128}}}
{{{t = 3.2 }}}

So the time of the first trip is t=3.2 hours. The return trip takes 48 minutes (or 0.8 hours) longer. 

t = 3.2 + 0.8
t = 4 hours

The return trip takes 4 hours.

We can then find the distance between Chicago and LA by using the d = vt equation:

{{{d = 640*3.2}}}
{{{d=2048}}}

So the distance is d = 2048 miles.