Question 771446
Let {{{ d }}} = the length of the track in meters
Let {{{ t }}} = the time spent sprinting in seconds
Convert minutes to seconds:
{{{ 2*60 = 120 }}} sec
{{{ 120 + 24 = 144 }}} sec
{{{ 144 - t }}} = time spent jogging in seconds
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Equation for sprinting:
(1) {{{ d = 6t }}}
Equation for jogging:
(2) {{{ d = 2*( 144 - t ) }}}
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(2) {{{ d = 288 - 2t }}}
By substitution:
(2) {{{ 6t = 288 - 2t }}}
(2) {{{ 8t = 288 }}}
(2) {{{ t = 36 }}} sec
and
(1) {{{ d = 6t }}}
(1) {{{ d = 6*36 }}}
(1) {{{ d = 216 }}}
The track is 216 meters long
check:
(2) {{{ d = 2*( 144 - t ) }}}
(2) {{{ 216 = 2*( 144 - 36 ) }}}
(2) {{{ 216 = 2*108 }}}
(2) {{{ 216 = 216 }}}
OK