Question 1046697
You can think of this as one of the cyclists
standing still and the other one moving
at the sum of their speeds
Let {{{ t }}} = the time in hrs for them to be 
{{{ 66 }}} mi apart
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{{{ 66 = ( 10 + 12 )*t }}}
{{{ 22t = 66 }}}
{{{ t = 3 }}} hrs
In 3 hrs they will be 66 mi apart
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check:
(1) {{{ d[1] = 10t }}}
(1) {{{ d[1] = 10*3 }}}
(1) {{{ d[1] = 30 }}}
and
(2) {{{ d[2] = 12*3 }}}
(2) {{{ d[2] = 36 }}}
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{{{ d[1] + d[2] = 66 }}}
{{{ 30 + 36 = 66 }}}
{{{ 66 = 66 }}}
OK