Question 573698
Let {{{ s }}} = his speed going uphill ( m/min )
{{{ 2s }}}= his speed going downhill ( m/min )
Let {{{ t }}} = His time going up hill ( min )
{{{ 4 - t }}} = his time going downhill ( min )
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uphill:
(1) {{{ 600 = s*t }}}
downhill:
(2) {{{ 400 = 2s*( 4 - t ) }}}
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(1) {{{ s = 600/t }}}
Substitute (1) into (2)
(2) {{{ 400 = 2*( 600/t )*(4 - t ) }}}
(2) {{{ 400 = ( 8 - 2t )*(600/t) }}}
(2) {{{ 400 = 4800/t - 1200 }}}
(2) {{{ 400t = 4800 - 1200t }}}
(2) {{{ 1600t = 4800 }}}
(2) {{{ t = 3 }}}
It takes him 3 minutes to reach the summit
check:
(1) {{{ s = 600/t }}}
(1) {{{ s = 600/3 }}}
(1) {{{ s = 200 }}}
and
(2) {{{ 400 = 2s*( 4 - t ) }}}
(2) {{{ 400 = 2*200*( 4 - 3 ) }}}
(2) {{{ 400 = 400 }}}
OK