Question 1139188
Let {{{ s }}} = the speed he actually went
(1) {{{ d = ( s + 18 )*( t - 15 ) }}}
(2) {{{ d = s*t }}}
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(2) {{{ s = d/t }}}
(1) {{{ d = ( d/t + 18 )*( t - 15 ) }}}
(1) {{{ 120 = ( 120/t + 18 )*( t - 15 ) }}}
(1) {{{ 120 = 120 + 18t - 1800/t - 270 }}}
(1) {{{ 270 = 18t - 1800/t }}}
(1) {{{ 270t = 18t^2 - 1800 }}}
(1) {{{ 18t^2 - 270t - 1800 = 0 }}}
(1) {{{ t^2 - 15t - 100 = 0 }}}
(1) {{{ ( t - 20 )*( t + 5 ) = 0 }}}
{{{ t = 20 }}}
and
{{{ 120 = s*20 }}}
{{{ s = 6 }}}
He rode 6 mi/hr
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check:
(1) {{{ 120 = ( 120/t + 18 )*( t - 15 ) }}}
(1) {{{ 120 = ( 120/20 + 18 )*( 20 - 15 ) }}}
(1) {{{ 120 = ( 6 + 18 )*5 }}}
(1) {{{ 120 = 24*5 }}}
(1) {{{ 120 = 120 }}}