Question 451180
  <pre><font face = "Tohoma" size = 4 color = "indigo"><b> 
Hi,
A cyclist bikes x distance at 10 miles per hour 
and returns over the same path at 8 miles per hour. (total distance is 2x)
Average rate = total distance/total time:  
Note t = D/r  t(going) = x/10mph,  t(returning) = x/8mph
Average rate = {{{2x/(x/10mph + x/8mph) = 2x/(4x/40 + 5x/40)}}}  
{{{2x/(9x/40) = 80/9 = 8.9 )}}}

For ex: If the cyclist went 40mi and biked back... 
 Average rate = total distance/total time =  80/(40/10 + 40/8) = 80/(4+5) = 80/9