Question 1027769
Let {{{ t }}} = his time in hours going to the meeting
Let {{{ s }}} = his speed in mi/hr going to the meeting
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Equation for going to the meeting
(1) {{{ 120 = s*t }}}
Equation for returning from the meeting
(2) {{{ 120 = ( s - 12 )*( 4 - t ) }}}
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(1) {{{ t = 120/s }}}
and
(2) {{{ 120 = 4s - 48 - s*t + 12t }}}
(2) {{{ 120 = 4s - 48 + t*( 12 - s ) }}}
(2) {{{ 120 = 4s - 48 + ( 120/s )*( 12 - s ) }}}
(2) {{{ 120 + 48 = 4s + 1440/s - 120 }}}
(2) {{{ 120 - 48 + 120 = 4s + 1440/s
(2) {{{ 288 = 4s + 1440/s }}}
(2) {{{ 288s = 4s^2 + 1440 }}}
(2) {{{ 4s^2 - 288s + 1440 = 0 }}}
(2) {{{ s^2 -72s + 360 = 0 }}}
Complete the square:
(2) {{{ s^2 -72s + ( -72/2)^2 = -360 + ( -72/2 )^2 }}}
(2) {{{ s^2 -72s + 1296 = -360 + 1296 }}}
(2) {{{ s^2 -72s + 1296 = 936 }}}
(2) {{{ ( s - 36 )^2 = 30.594^2 }}}
(2) {{{ s - 36 = 30.594 }}}
(2) {{{ s = 30.594 + 36 }}}
(2) {{{ s = 66.594 }}}
he traveled at 66.6 mi/hr to the city
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check:
(1) {{{ 120 = s*t }}}
(1) {{{ 120 = 66.594t }}}
(1) {{{ t = 1.802 }}} hrs
and
(2) {{{ 120 = ( s - 12 )*( 4 - t ) }}}
(2) {{{ 120 = ( 66.594 - 12 )*( 4 - t ) }}}
(2) {{{ 120 = 54.594*( 4 - t ) }}}
(2) {{{ 120 = 218.376 - 54.594t }}}
(2) {{{ 218.376 - 120 = 54.594t }}}
(2) {{{ 54.594t = 98.376 }}}
(2) {{{ t = 1.802 }}} hrs
OK
check the math