Question 667136
Call the length of the trip in miles {{{ d }}}
One-third of the way is {{{ d/3 }}}
One-sixth of the way is {{{ d/6 }}}
given:
{{{ d/3 + 10 + d/6 = d }}}
Multiply both sides by {{{ 6 }}}
{{{ 2d + 60 + d = 6d }}}
{{{ 3d = 60 }}}
{{{ d = 20 }}}
The trip was 20 miles
check:
{{{ d/3 + 10 + d/6 = d }}}
{{{ 20/3 + 10 + 20/6 = 20 }}}
{{{ 6 + 2/3 + 10 + 3 + 1/3 = 20 }}}
{{{ 10 + 6 + 3 + 1 = 20 }}}
{{{ 20 = 20 }}}
OK