Question 884367
Let {{{ r }}} = the rate of each car in mi/hr
In 2 hrs, the 1st car has traveled
{{{ d[1] = r*2 }}}
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The 2nd car leaves after 2 hrs, so
10 AM + 2 hrs = 12 AM
From 12 AM to 4 PM is 4 hrs
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Let {{{ d }}} = the distance the 2nd car
travels in 4 hrs
{{{ 450 - d - 2r  }}} = the distance the 1st has
traveled in 4 hrs
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Equation for the 2nd car:
(1) {{{ d = r*4 }}}
Equation for 1st car:
(2) {{{ 450 - d - 2r = r*4 }}}
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Note that equations are for 12 AM to 4 PM only
Substitute (1) into (2)
(2) {{{ 450 - r*4 - 2r = r*4 }}}
(2) {{{ 10r = 450 }}}
(2) {{{ r = 45 }}}
The rate of the cars was 45 mi/hr
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check:
(1) {{{ d = r*4 }}}
(1) {{{ d = 45*4 }}}
(1) {{{ d = 180 }}}
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(2) {{{ 450 - d - 2r = r*4 }}}
(2) {{{ 450 - d - 2*45 = 45*4 }}}
(2) {{{ 450 - d - 90 = 180 }}}
(2) {{{ d = 450 - 90 - 180 }}}
(2) {{{ d = 450 - 270 }}}
(2) {{{ d = 180 }}}
OK