Question 632407
Let {{{ t }}} = the Wolf's time to get there in hours
Let {{{ s }}} = Wolf's average speed in mi/hr
given:
RRH's equation:
(1) {{{ 432 = ( s + 6 )*( t - 1 ) }}}
Wolf's equation:
(2) {{{ 432 = s*t }}}
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(1) {{{ 432 = s*t + 6t - s - 6 }}}
and
(2) t = 432/s }}}
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Substitute (2) into (1)
(1) {{{ 432 = s*(432/s) + 6*(432/s) - s - 6 }}}
Multiply both sides by {{{ s }}}
(1) {{{ 432s = 432s + 2592- s^2 - 6s }}}
(1) {{{ s^2 + 6s - 2592 = 0 }}}
Use quadratic equation
{{{s = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = 1 }}}
{{{ b = 6 }}}
{{{ c = -2592 }}}
{{{s = (-6 +- sqrt( 6^2-4*1*(-2592) ))/(2*1) }}}
{{{s = ( -6 +- sqrt( 36 + 10368 ))/2 }}}
{{{s = ( -6 +- sqrt( 10404 ))/2 }}}
{{{ s = ( -6 + 102 ) /2 }}} ( ignore the negative square root )
{{{ s = 96/2 }}}
{{{ s = 48 }}}
RRH's speed was 48 mi/hr
check answer:
(2) {{{ 432 = s*t }}}
(2) {{{ 432 = 48*t }}}
(2) {{{ t = 9 }}} hrs
and
(1) {{{ 432 = ( s + 6 )*( t - 1 ) }}}
(1) {{{ 432 = ( s + 6 )*( 9 - 1 ) }}}
(1) {{{ 432 = 8*( s + 6 ) }}}
(1) {{{ s + 6 = 54 }}}
(1) {{{ s = 48 }}}
OK