Question 473957
Let {{{ s }}} = biker's speed going to city
given:
Time going to city is {{{ t = 2.7 }}} hrs
{{{ d = s*t }}}
{{{ d = s*2.7 }}}
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Coming back from city is the same distance, so
{{{ d = ( s - 3)*(2.7 + .9) }}}
{{{ d = 2.7s - 8.1 + .9s - 2.7 }}}
{{{ d = 3.6s - 10.8 }}}
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Since the distances are equal,
{{{ s*2.7 = 3.6s - 10.8 }}}
Subtract {{{ 2.7s }}} from both sides
{{{ 0 = .9s - 10.8 }}}
Add {{{ 10.8 }}} to both sides
{{{ .9s = 10.8 }}}
{{{ s = 12 }}}
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Now find {{{ d }}}
{{{ d = 2.7s }}}
{{{ d = 2.7*12 }}}
{{{ d = 32.4 }}}
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Since the biker went to the city and 
then back again, you need to find {{{ 2d }}}
{{{ 2d = 2*32.4 }}}
{{{ 2d = 64.8 }}}
The total distance biked is 64.8 mi
check:
{{{ d = ( s - 3)*(2.7 + .9) }}}
{{{ d = ( 12 - 3)*(2.7 + .9) }}}
{{{ d = 9*3.6 }}}
{{{ d = 32.4 }}}
{{{ 2d = 64.8 }}}
OK