Question 544531
Average speed is always ( total distance ) / ( total time )
Call the distance between A and B {{{d}}}
Let {{{r}}} = rate on B to A trip
Going from A to B:
{{{ d = 30t[1] }}}
{{{ t[1] = d/30 }}}
Going from B to A:
{{{ d = r*t[2] }}}
{{{ t[2] = d/r }}}
The average speed is
{{{ (2d) / ( t[1] + t[2] ) }}}
{{{ (2d) / (d/30 + d/r ) }}}
Divide top and bottom by {{{d}}}
{{{ 2 / ( 1/30 + 1/r ) }}}
If average speed is {{{60}}} mi/hr,
{{{ 60 = 2 / ( 1/30 + 1/r ) }}}
{{{ 60*( 1/30 + 1/r ) = 2 }}}
{{{ 2 + 60/r = 2 }}}
{{{ 60/r = 0 }}}
{{{ r }}} has to be infinite, so you can't possibly average 60 mi/hr
check: What if average speed must be 59 mi/hr?
{{{ 59 = 2 / ( 1/30 + 1/r ) }}}
{{{ 59*(1/30 + 1/r ) = 2 }}}
{{{ 59/30 + 59/r = 2 }}}
{{{ 59/r = 60/30 - 59/30 }}}
{{{ 59/r = 1/30 }}}
Multiply both sides by {{{30r}}}
{{{ 59*30 = r }}}
{{{  r = 1770 }}} mi/hr
This is OK for a rocket to space, but not a vehicle.
The average speed needs to be lower still