Question 1016791
Let {{{ s }}} = his speed in mi/hr for 
driving during rainstorm
Let {{{ t }}} = his time in hrs for
driving during rainstorm
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Equation for driving during rainstorm:
(1) {{{ 252 = s*t }}}
Equation for driving after rainstorm:
(2) {{{ 144 = ( s+6 )*( 9 - t ) }}}
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(1) {{{ t = 252/s }}}
and
(2) {{{ 144 = 9s + 54 - s*t - 6t }}}
(2) {{{ 144 = 9s + 54 - t*( s + 6 ) }}}
(2) {{{ 144 = 9s + 54 -( 252/s )*( s + 6 ) }}}
(2) {{{ 144 = 9s + 54 - 252 - 1512/s }}}
(2) {{{ 144 + 252 - 54 = 9s - 1512/s }}}
(2) {{{ 342 = 9s - 1512/s }}}
(2) {{{ 342s = 9s^2 - 1512 }}}
(2) {{{ 9s^2 - 342s - 1512 = 0 }}}
(2) {{{ s^2 - 38s - 168 = 0 }}}
Use quadratic equation
{{{ s = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{ a = 1 }}}
{{{ b = -38 }}}
{{{ c = -168 }}}
{{{ s = (-(-38) +- sqrt( (-38)^2-4*1*(-168) ))/(2*1) }}} 
{{{ s = ( 38 +- sqrt( 1444 + 672 ))/2 }}} 
{{{ s = ( 38 +- sqrt( 2116 ))/2 }}} 
{{{ s = ( 38 + 46)/2 }}} 
{{{ s = 84/2 }}}
{{{ s = 42 }}}
and
{{{ s + 6 = 48 }}}
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His speed during rainstorm was 42 mi/hr
His speed after rainstorm was 48 mi/hr
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check:
(1) {{{ 252 = s*t }}}
(1) {{{ 252 = 42t }}}
(1) {{{ t = 6 }}} hrs
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(2) {{{ 144 = ( s+6 )*( 9 - t ) }}}
(2) {{{ 144 = 48*( 9 - t ) }}}
(2) {{{ 144 = 432 - 48t }}}
(2) {{{ 48t = 288 }}}
(2) {{{ t = 6 }}} hrs
OK