Question 880137
(1) {{{ 100 = r*t }}}
(2) {{{ 100 = ( r+5 )*( t-1 ) }}}
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(1) {{{ t = 100/r }}}
By substitution:
(2) {{{ 100 = ( r + 5 )*( 100/r - 1 ) }}}
(2) {{{ 100 = 100 + 500/r - r - 5 }}}
(2) {{{ r + 5 = 500/r }}}
(2) {{{ r^2 + 5r = 500 }}}
(2) {{{ r^2 + 5r + ( 5/2)^2 = 500 + (5/2)^2 }}}
(2) {{{ r^2 + 5r + 25/4 = 2000/4 + 25/4 }}}
(2) {{{ r^2 + 5r + 25/4 = 2025/4 }}}
(2) {{{ ( r + 5/2 )^2 = ( 45/2 )^2 }}}
(2) {{{ r + 5/2 = 45/2 }}}
(2) {{{ r = 40/2 }}}
(2) {{{ r = 20 }}}
The car's original speed was 20 mi/hr
check:
(1) {{{ 100 = r*t }}}
(1) {{{ 100 = 20t }}}
(1) {{{ t = 5 }}}
and
(2) {{{ 100 = ( r+5 )*( t-1 ) }}}
(2) {{{ 100 = ( 20+5 )*( t-1 ) }}}
(2) {{{ 100 = 25t - 25 }}}
(2) {{{ 25t = 125 }}}
(2) {{{ t = 5 }}}
OK