Question 1086524
Let {{{ r }}} = the rate walking in mi/hr
{{{ 10r }}} = the rate driving the car
Let {{{ t }}} = the time in hrs spent driving
{{{ t - 2 }}} = the time in hrs spent walking
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Equation for walking:
(1) {{{ 4 = r*( t - 2 )  }}}
Equation for driving:
(2) {{{ 120 = 10r*t }}}
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(2) {{{ r = 12/t }}}
Plug (2) into (1)
(1) {{{ 4 = ( 12/t )*( t-2 ) }}}
(1) {{{ 4t = 12*( t-2 ) }}}
(1) {{{ 4t = 12t - 24 }}}
(1) {{{ 8t = 24 }}}
(1) {{{ t = 3 }}} hrs
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The motorist took 3 hrs to drive the 120 mi
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check:
(2) {{{ 120 = 10r*t }}}
(2) {{{ 120 = 10r*3 }}}
(2) {{{ 3r = 12 }}}
(2) {{{ r = 4 }}} mi/hr
and
(1) {{{ 4 = r*( t - 2 )  }}}
(1) {{{ 4 = r*( 3 - 2 )  }}}
(1) {{{ r = 4 }}} mi/hr
OK