Question 1018185
Let {{{ s }}} = the speed of the car taking 
the shorter route in mi/hr
{{{ s - 2 }}} = the speed of the cat taking the 
longer route in mi/hr
Let {{{ d }}} = the distance of the shorter route in miles
{{{ d + 43 }}} = the distance of the longer route in miles
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Equation for car taking the shorter route:
(1) {{{ d = s*5 }}}
euation for the car taking the longer route:
(2) {{{ d + 43 = ( s-2 )*6 }}}
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Substitute (1) into (2)
(2) {{{ s*5 + 43 = ( s-2 )*6 }}}
(2) {{{ 5s + 43 = 6s - 12 }}}
(2) {{{ s = 55 }}}
and
{{{ s - 2 = 53 }}}
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(1) {{{ d = s*5 }}}
(1) {{{ d = 55*5 }}}
(1) {{{ d = 275 }}}
and
(2) {{{ d + 43 = ( s-2 )*6 }}}
(2) {{{ d + 43 = (55-2 )*6 }}}
(2) {{{ d + 43 = 53*6 }}}
(2) {{{ d + 43 = 318 }}}
The shorter route is 275 mi
The longer route is 318 mi
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check:
(2) {{{ d + 43 = 318 }}}
(2) {{{ d = 275 }}}
OK