Question 242908
A truck driver travels a certain distance at 60 miles per hour and returns over the same road at 40 miles per hour. What is her average rate for the round trip? 
I know it is a d=rt but I don't know where to begin. Can Please help by explaining thoroughly.
<pre><font size = 4 color = "indigo"><b>

Notice that you are NOT given the distance, but the distance will not
matter, because the answer is independent of the distance.  However
we have to let distance be a variable d anyway.

Make this chart:

             Distance      Rate       Time
Going
Returning
---------------------------------------------
Totals                     XXXX 

Fill in the distances, which are both d

             Distance      Rate       Time
Going           d            
Returning       d          
----------------------------------------------
Totals                     XXXX                     

Fill in their total 2d

             Distance      Rate       Time
Going           d           
Returning       d          
----------------------------------------------
Totals         2d          XXXX     

Fill in the rates, which are 60 and 40


             Distance      Rate       Time
Going           d           60      
Returning       d           40        
----------------------------------------------
Totals         2d          XXXX     

Use the formula {{{TIME=(DISTANCE)/(RATE)}}} to fill
in the times:

             Distance      Rate       Time 
Going           d           60        d/60 
Returning       d           40        d/40
----------------------------------------------
Totals         2d          XXXX       

Total up the times

             Distance      Rate       Time
Going           d           60        d/60 
Returning       d           40        d/40
----------------------------------------------
Totals         2d          XXXX     d/60 + d/40  


Now to calculate the average rate

Average rate = {{{(total_distance)/(total_time) = (2d)/(d/60+d/40) }}} 

To simplify that complex fraction, multiply top and bottom by 120:

{{{(2d)/(d/60+d/40) }}}

{{{(120*2d)/((120d)/60+(120d)/40) }}}

{{{(240d)/(2d+3d)}}}

{{{240d/(5d)}}}

{{{(240cross(d))/(5cross(d))}}}

See how the d's canceled?  That shows it didn't matter what the
distance d was, and there is no way of finding out because it
could be any number of miles.

{{{240/5}}}

{{{48}}}miles per hour.

Edwin</pre>