Question 1085594
What was Sarah's head start in miles?
{{{ d = r*t }}}
{{{ d[1] = 24*2 }}}
{{{ d[1] = 48 }}} mi
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Start a stopwatch when Jane leaves and stop it
when she catches up with Sarah
( note that it is 8:30 AM when Jane leaves
Let {{{ t }}} = the time on the stopwatch in hours
Let {{{ d }}} = the distance in miles that Jane
travels until she ctches up with Sarah
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Jane's equation:
(1) {{{ d = 40t }}}
Sarah's equation:
(2) {{{ d - 48 = 24t }}}
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Plug (1) into (2)
(2) {{{ 40t - 48 = 24t }}}
(2) {{{ 16t = 48 }}}
(2) {{{ t = 3 }}}
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8:30 plus 3 hrs is 11:30 when
Jane catches up with Sarah
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check:
(1) {{{ d = 40t }}}
(1) {{{ d = 40*3 }}}
(1) {{{ d = 120 }}} mi
and
(2) {{{ d - 48 = 24t }}}
(2) {{{ d - 48 = 24*3 }}}
(2) {{{ d = 48 + 72 }}}
(2) {{{ d = 120 }}} mi
OK
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