Question 1039828
How much of a head start in miles did Mr. Smith have?
{{{ d[1] = 60*4 }}}
{{{ d[1] = 240 }}} mi
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Start a stopwatch when Mrs. Smith leaves. Let {{{ t }}}
= the time on the stopwatch in hrs when Mrs. Smith
catches up with Mr. Smith.
Let {{{ d }}} = the distance in miles that Mrs. Smith
travels until she overtakes Mr. Smith
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Mr. Smith's equation:
(1) {{{ d - 240 = 60t }}}
Mrs. Smith's equation:
(2) {{{ d = 80t }}}
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Substitute (2) into (1)
(1) {{{ 80t - 240 = 60t }}}
(1) {{{ 20t = 240 }}}
(1) {{{ t = 12 }}} 
Mrs. Smith overtakes Mr. Smith in 12 hrs
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check:
(2) {{{ d = 80t }}}
(2) {{{ d = 80*12 }}}
(2) {{{ d = 960 }}} mi
and
(1) {{{ d - 240 = 60t }}}
(1) {{{ d - 240 = 60*12 }}}
(1) {{{ d = 240 + 720 }}}
(1) {{{ d = 960 }}} mi
OK