Question 1009262
Let {{{ t }}} = time in hrs for her to bicycle
5 times around the loop
{{{ 1.75 - t }}} = time in hrs for her to
run around loop 1 time
Let {{{ d }}} = the distance of the loop in miles
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Her equation for running:
(1) {{{ d = 8*( 1.75 - t ) }}}
Her equation for bicycling:
(2) {{{ 5d = 16t }}}
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(1) {{{ d = 14 - 8t }}}
Substitute (1) into (2)
(2) {{{ 5*( 14 - 8t ) = 16t }}}
(2) {{{ 70 - 40t = 16t }}}
(2) {{{ 56t = 70 }}}
(2) {{{ t = 1.25 }}}
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(2) {{{ 5d = 16t }}}
(2) {{{ 5d = 16*1.25 }}}
(2) {{{ 5d = 20 }}}
(2) {{{ d = 4 }}}
The distance of the loop is 4 mi
check:
(1) {{{ d = 8*( 1.75 - t ) }}}
(1) {{{ d = 8*( 1.75 -1.25 ) }}}
(1) {{{ d = 8*.5 }}}
(1) {{{ d = 4 }}}
OK