Question 498236
(1) {{{ (3/4)*r[1] + (2/3)*r[2] = 16 }}}
(2) {{{ (1/2)*r[1] + (4/5)*r[2] = 16 }}}
Multiply both sides of (1) by {{{12}}}
Multiply both sides of (2) by {{{10}}}
(1) {{{ 9r[1] + 8r[2] = 192 }}}
(2) {{{ 5r[1] + 8r[2] = 160 }}}
Subtract (2) from (1)
(1) {{{ 9r[1] + 8r[2] = 192 }}}
(2) {{{ -5r[1] - 8r[2] = -160 }}}
{{{ 4r[1] = 32 }}}
{{{ r[1] = 8 }}} km/hr
Plug this result back into (2)
(2) {{{ 5*8 + 8r[2] = 160 }}}
(2) {{{ 40 + 8r[2] = 160 }}}
(2) {{{ 8r[2] = 120 }}}
(2) {{{ r[2] = 15 }}} km/hr
He walks at 8 km/hr
He runs at 15 km/hr