Question 106385
This problem depends on the relationship between distance, rate, and time.  The formula for straight line travel is:


{{{d=rt}}}


What we don't know is the time, t or the distance, d.  But we can say that the distance from Los Angeles to Chicago is:

{{{d = 640t}}}



We can also say that the distance from Chicago to Los Angeles is given by:

{{{d = 512(t+48)}}}

since the return trip took 48 minutes longer.


The distance between the cities remains constant regardless of the direction of travel, so we can say:

{{{640t = 512(t+48)}}}


Solving:

{{{640t - 512t = 24576}}}
{{{128t = 24576}}}
{{{t=192}}}

Therefore the elapsed time for the Los Angeles to Chicago trip was 192 minutes, and the elapsed time for the Chicago to Los Angeles trip was 48 minutes longer, or 240 minutes, or 4 hours.

Now that we know the time value for each of the rates, we can use the same formula {{{d=rt}}} to calculate the remaining variable, d.

{{{(512mph)(4 hrs)= 2048 miles}}}


To check the answer:

{{{192/60=3.2}}}

{{{(640mph)(3.2hrs)=2048miles}}}

Which just goes to prove that no one picked Los Angeles up and moved it while you were visiting Chicago.