Question 1055874
Let {{{ t }}} = time in hrs to run on the downhill part
{{{ 1 - t }}} = time in hrs to run on level ground
{{{ s }}} = speed in mi/hr running downhill
{{{ s - 3 }}} = speed in mi/hr running on level ground
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Equation for funning on level ground:
(1) {{{ 4 = ( s - 3 )*( 1 - t ) }}}
Equation for running downhill:
(2) {{{ 3 = s*t }}}
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(2) {{{ t = 3/s }}}
Plug (2) into (1)
(1) {{{ 4 = ( s - 3 )*( 1 - 3/s ) }}}
(1) {{{ 4 = s - 3 - 3 + 9/s }}}
(1) {{{ 10 = s + 9/s }}}
Multiply both sides by {{{ s }}}
(1) {{{ 10s = s^2 + 9 }}}
(1) {{{ s^2 - 10s + 9 = 0 }}}
(1) {{{ ( s - 9 )*( s - 1 ) = 0 }}} ( by looking at it )
I have to choose between
{{{ s = 9 }}} and
{{{ s = 1 }}}
it can't be {{{ s = 1 }}} since
{{{ s - 3 }}} = speed in mi/hr running on level ground
and I would end up with negative speed
So, {{{ s = 9 }}}
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She runs 9 mi/hr on the downhill part
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check:
(2) {{{ t = 3/s }}}
(2) {{{ t = 3/9 }}}
(2) {{{ t = 1/3 }}}
and
(1) {{{ 4 = ( s - 3 )*( 1 - t ) }}}
(1) {{{ 4 = ( 9 - 3 )*( 1 - t ) }}}
(1) {{{ 4 = 6*( 1 - t ) }}}
(1) {{{ 4 = 6 - 6t }}}
(1) {{{ 6t = 6 - 4 }}}
(1) {{{ 6t = 2 }}}
(1) {{{ t = 1/3 }}}
OK