Question 1065246
I think I will end up with 4 equations and 4 unknowns,
which means it is solvable
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For the 1st day:
Let the time for the 24 km trip be {{{ t[1] }}} hrs
The time for the 40 km trip is {{{ 9 - t[1] }}} hrs
For the 2nd day:
Let the time for the 18 km trip be {{{ t[2] }}} hrs
The time for the 48 km trip is {{{ 9 - t[2] }}} hrs
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That gives me the 4 unknowns:
{{{ x }}}, {{{ y }}}, {{{ t[1]}}}, and {{{ t[2] }}}
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(1 ) {{{ 24 = x*t[1] }}}
(2) {{{ 40 = y*( 9 - t[1] ) }}}
(3) {{{ 18 = x*t[2] }}}
(4) {{{ 48 = y*( 9 - t[2] ) }}}
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(2) {{{ y = 40/( 9 - t[1] ) }}}
Substitute this into (4)
(4) {{{ 48 = ( 40/( 9 - t[1] ) )*( 9 - t[2] ) }}}
(4) {{{ 48*( 9 - t[1] ) = 40*( 9 - t[2] ) }}}
(4) {{{ 6*( 9 - t[1] ) = 5*( 9 - t[2] ) }}}
(4) {{{ 54 - 6t[1] = 45 - 5t[2] }}}
(4) {{{ 6t[1] - 5t[2] = 9 }}}
and
(1) {{{ x = 24/t[1] }}}
Substitute into (3)
(3) {{{ 18 = ( 24/t[1] )*t[2] }}}
(3) {{{ 18t[1] = 24t[2] }}}
(3) {{{ 3t[1] = 4t[2] }}}
(3) {{{ t[2] = (3/4)*t[1] }}}
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Substitute (3) into (4)
(4) {{{ 6t[1] - 5*(3/4)*t[1] = 9 }}}
(4) {{{ (24/4)*t[1] - (15/4)*t[1] = 9 }}}
(4) {{{ 24t[1] - 15t[1] = 36 }}}
(4) {{{ 9t[1] = 36 }}}
(4) {{{ t[1] = 4 }}} hrs
and
(3) {{{ t[2] = (3/4)*t[1] }}}
(3) {{{ t[2] = (3/4)*4 }}}
(3) {{{ t[2] = 3 }}} hrs
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(1 ) {{{ 24 = x*t[1] }}}
(1 ) {{{ 24 = x*4 }}}
(1 ) {{{ x = 6 }}} km/hr
and
(2) {{{ 40 = y*( 9 - t[1] ) }}}
(2) {{{ 40 = y*( 9 - 4 ) }}}
(2) {{{ 40 = y*5 }}}
(2) {{{ y = 8 }}} km/hr
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check answers:
(3) {{{ 18 = x*t[2] }}}
(3) {{{ 18 = x*3 }}}
(3) {{{ x = 6 }}}
and
(4) {{{ 48 = y*( 9 - t[2] ) }}}
(4) {{{ 48 = y*( 9 - 3 ) }}}
(4) {{{ 48 = y*6 }}}
(4) {{{ y = 8 }}}
OK