Question 735018
Actual trip:
{{{ d = r*t }}}
(1) {{{ 2 = r*t }}}
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"what if " trip:
(2) {{{ 2 = ( r + 7 )*( t - 3 ) }}}
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There are 2 equations and 2 unknowns, 
so it's solvable
(2) {{{ 2 = r*t + 7t - 3r - 21 }}}
and
(1) {{{ t = 2/r }}}
By substitution:
(2) {{{ 2 = r*(2/r) + 7*(2/r) - 3r - 21 }}}
(2) {{{ 2 = 2 + 14/r - 3r - 21 }}}
(2) {{{ 3r + 21 = 14/r }}}
Multiply both sides by {{{ r }}}
(2) {{{ 3r^2 + 21r = 14 }}}
(2) {{{ 3r^2 + 21r - 14 = 0 }}}
Use quadratic formula
{{{ r = ( -b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = 3 }}}
{{{ b = 21 }}}
{{{ c = -14 }}}
{{{ r = ( -21 +- sqrt( 21^2 - 4*3*(-14) )) / (2*3) }}}
{{{ r = ( -21 +- sqrt( 441 + 168 )) / 6 }}}
{{{ r = ( -21 +- sqrt( 609 )) / 6 }}}
{{{ r = ( -21 + 24.68 ) / 6 }}}
{{{ r = 3.68/6 }}}
{{{ r = .6133 }}}
She traveled .6133 km/hr
check:
(1) {{{ 2 = r*t }}}
{{{ t = 2/.6133 }}}
{{{ t = 3.26 }}} hrs
and
(2) {{{ 2 = ( r + 7 )*( t - 3 ) }}}
(2) {{{ 2 = ( .6133 + 7 )*( 3.26 - 3 ) }}}
(2) {{{ 2 = 7.6133*.26 }}}
(2) {{{ 2 = 1.979 }}}
I think the error is due to rounding off