Question 1005986
Let {{{ s }}} = the speed of the bicycle
{{{ s + 38.6 }}} = the speed of the car
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Think of this as one of them standing still
( either one ) and the other traveling at 
the sum of their speeds
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{{{ 570 = ( s + s + 38.6 )*9.5 }}}
{{{ 570 = 19s + 366.7 }}}
{{{ 19s = 203.3 }}}
{{{ s = 10.7 }}}
and
{{{ s + 38.6 = 10.7 + 38.6 }}}
{{{ s + 38.6 = 49.3 }}}
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their speeds are:
10.7 mi/hr and 49.3 mi/hr
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check:
{{{ 570 = ( 2s + 38.6 )*9.5 }}}
{{{ 570 = ( 2*10.7 + 38.6 )*9.5 }}}
{{{ 570 = ( 21.4 + 38.6 )*9.5 }}}
{{{ 570 = 60*9.5 }}}
{{{ 570 = 570 }}}
OK