Question 947363
Average rate is always ( total distance ) / ( total time )
The total distance is:
{{{ 60 + 60 = 120 }}} mi
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Time for Fox - Nenana trip:
{{{ t = d/r }}}
{{{ t = 60/30 }}}
{{{ t = 2 }}} hrs
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Time for Nenana - Fox trip:
Let {{{ r }}} = the rate for this trip
{{{ t = 60/r }}}
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The total time is:
{{{ 2 + 60/r }}}
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Average for the whole trip =
{{{ 60 }}} mi/hr
{{{ 60 }}} = ( total distance ) / ( total time )
{{{ 60 = 120 / ( 2 + 60/r ) }}}
Multiply both sides by {{{ 2 + 60/r }}}
{{{ 60*( 2 + 60/r ) = 120 }}}
{{{ 2 + 60/r = 2 }}}
{{{ 60/r = 0 }}}
{{{ r }}} = infinity!
There is no way you can average {{{ 60 }}} mi/hr
with the data given
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Suppose your speed for Fox - Nenana was
{{{ 31 }}} mi/hr instead of {{{ 30 }}} mi/hr
{{{ t = 60/31 }}}
{{{ t = 1.9355 }}} hrs
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Then you end up with:
{{{ 60 = 120/( 1.9355 + 60/r ) }}}
{{{ 60*( 1.9355 + 60/r ) = 120 }}}
{{{ 1.9355 + 60/r = 2 }}}
{{{ 60/r = .0645 }}}
{{{ r = 60/.0645 }}}
{{{ r = 930.233 }}}
Now your speed doesn't have to be infinite,
but it is still impossible
You have to make the trip back at
something like {{{ 60 }}} mi/hr