Question 672809
Let {{{ r }}} = his rate on the freeway
{{{ r + 9 }}} = his rate on side roads
Let {{{ t }}} = time for both
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On side roads:
(1) {{{ 25 = ( r + 9 )*t }}}
On freeway:
(2) {{{ 20 = r*t }}}
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(1) {{{ 25 = r*t + 9t }}}
Substitute (2) into (1)
(1) {{{ 25 = 20 + 9t }}}
(1) {{{ 9t = 5 }}}
(1) {{{ t = 5/9 }}}
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On side roads:
(1) {{{ 25 = ( r + 9 )*(5/9) }}}
(1) {{{ 25 = (5/9)*r + 5 }}}
(1) {{{ (5/9)*r = 20 }}}
(1) {{{ r = (9/5)*20 }}}
(1) {{{ r = 36 }}}
{{{ r + 9 = 45 }}}
His rate on side roads is 45 mi/hr
check:
(2) {{{ 20 = r*t }}}
(2) {{{ 20 = 36*(5/9) }}}
(2) {{{ 180 = 180 }}}