Question 971576
Let {{{ d }}} = distance Bob walked at {{{ 2 }}} mi/hr
{{{ 2.5 - d }}} = distance he walked at {{{ 4 }}} mi/hr
Let {{{ t }}} = total time he walked on treadmill
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Walking at 2 mi/hr:
(1) {{{ d = 2*( 1/3 )*t }}}
Walking at 4 mi/hr
(2) {{{ 2.5 - d = 4*( 2/3 )*t }}}
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Substitute (1) into (2)
(2) {{{ 2.5 - 2*(1/3)*t = 4*( 2/3 )*t }}}
(2) {{{ ( 8/3 )*t + ( 2/3 )*t = 2.5 }}}
(2) {{{ ( 10/3 )*t = 10/4 }}}
(2) {{{ t/3 = 1/4 }}}
(2) {{{ t = 3/4 }}}
He was on the treadmill for 3/4 hr or 45 min
check:
(1) {{{ d = 2*( 1/3 )*t }}}
(1) {{{ d = 2*( 1/3 )*(3/4) }}}
(1) {{{ d = 1/2 }}} mi
and
(2) {{{ 2.5 - d = 4*( 2/3 )*t }}}
(2) {{{ 2.5 - 1/2 = 4*( 2/3 )*t }}}
(2) {{{ 2 = 4*( 2/3 )*t }}}
(2) {{{ 6 = 8t }}}
(2) {{{ t = 3/4 }}} hr
OK