Question 438390
Let {{{d}}} = highway miles he has to drive
In words:
(total miles driven)/(gallons used) = efficiency in mi/gal
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given:
Gallons of gas used in city = {{{ 150/18 = 25/3 }}}
Gallons of gas used on highway = {{{ d/24 }}}
{{{ (150 + d)/( 25/3 + d/24 ) = 20 }}}
{{{ (150 + d) / ((200 + d)/24) = 20 }}}
Multiply both sides by {{{  ((200 + d)/24) }}}
{{{ 150 + d = (5/6)*(200 + d) }}}
Multiply both sides by {{{6}}}
{{{ 900 + 6d = 1000 + 5d }}}
{{{ d = 1000 - 900 }}}
{{{ d = 100 }}}
He has to drive 100 miles on the highway
check answer:
{{{ (150 + d) / ((200 + d)/24) = 20 }}}
{{{ (150 + 100) / ((200 + 100)/24) = 20 }}}
{{{ 250 / (300/24) = 20 }}}
{{{ 250 = (20/24)*300 }}}
{{{ 24*250 = 6000 }}}
{{{ 6000 = 6000 }}}
OK