Question 1097199
Kayla's speed = {{{ 100/12 = 25/3 }}} yds/sec
Naomi's speed = {{{ 100/16 = 25/4 }}} yds/sec
Let {{{ d }}} = distance that Kayla runs
until she catches Naomi
Let {{{ t }}} = time in seconds until
Kayla catch up with Naomi
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Start a stop watch at {{{ t=0 }}}
when Kayla leaves
Naomi's head start is {{{ 20 }}} yds
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Kayla's equation:
(1) {{{ d = ( 25/3 )*t  }}}
Naomi's equation:
(2) {{{ d - 20 = ( 25/4 )*t }}}
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Plug (1) into (2)
{{{ (25/3)*t - 20 = ( 25/4 )*t }}}
Multiply both sides by {{{ 12 }}}
{{{ 100t - 240 = 75t }}}
{{{ 25t = 240 }}}
{{{ t = 240/25 }}}
{{{ t = 9.6 }}} sec
Kayla catches Naomi in 9.6 sec
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check:
(1) {{{ d = (25/3)*t }}}
(1) {{{ d = (25/3)*9.6 }}}
(1) {{{ d = 8.333*9.6 }}} 
(1) {{{ d = 80 }}} yds
and
(2) {{{ d - 20 = ( 25/4 )*t }}}
(2) {{{ d - 20 = 6.25*9.6 }}}
(2) {{{ d - 20 = 60 }}}
(2) {{{ d = 80 }}} yds
OK