Question 729735
Nancy has {{{ 1/4 }}} hr head start.
{{{ d[1] = 30*(1/4) = 7.5 }}} mi is her head start
Start a stopwatch when Mark leaves and stop
it when they are {{{ 165 }}} mi apart.
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Let {{{ t }}} = the time on the stopwatch when stopped
Let {{{ d }}} = distance in miles Nancy travels in time {{{ t }}}
{{{ 165 - ( d + 7.5 ) }}} = distance in miles Mark travels in time {{{ t }}}
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Nancy's equation:
(1) {{{ d =  30t }}}
Mark's equation:
(2) {{{ 165 - ( d + 7.5 ) = 40t }}}
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(2) {{{ 165 - d - 7.5 = 40t }}}
(2) {{{ d + 40t = 157.5 }}}
Substitute (1) into (2)
(2) {{{ 30t + 40t = 157.5 }}}
(2) {{{ 70t = 157.5 }}}
(2) {{{ t = 2.25 }}}
7:15 AM + 2.25 hrs = 9:40 AM
They are 165 mi apart at 9:40 AM
check:
(1) {{{ d =  30t }}}
(1) {{{ d =  30*2.25 }}}
(1) {{{ d = 67.5 }}}
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(2) {{{ 165 - ( d + 7.5 ) = 40t }}}
(2) {{{ 165 - ( d + 7.5 ) = 40*2.25 }}}
(2) {{{ 165 - 7.5 - d = 90 }}}
(2) {{{ d = 165 - 97.5 }}}
(2) {{{ d = 67.5 }}}
OK