Question 1049381
What is Dan's head start in miles?
{{{ d[1] = 55*1 }}}
{{{ d[1] = 55 }}} mi
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Start a stopwatch when Joe leaves. Let
{{{ t }}} = time in hrs on stopwatch when
they are {{{ 300 }}} mi apart
Let {{{ d }}} = distance Joe travels until
they are {{{ 300 }}} mi apart
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Joe's equation:
(1) {{{ d = 50t }}}
Dan's equation:
(2) {{{ 300 - d -55 = 55t }}}
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Substitute (1) into (2)
(2) {{{ 300 - 50t - 55 = 55t }}}
(2) {{{ 105t = 245 }}}
(2) {{{ t = 2.333 }}} hr
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Dan will have traveled for 1 hr ( his head start ) plus
2 hrs and 20 min for a total of
3 hrs and 20 min
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check:
Joe travels a distance of:
(1) {{{ d = 50*2.333 }}}
(1) {{{ d = 116.667 }}}
and, in time {{{ t = 2.333 }}} hrs,
Dan traveled:
(2) {{{ 300 - d -55 = 55t }}}
(2) {{{ 300 - d -55 = 55*2.333 }}}
(2) {{{ 300 - d - 55 = 128.3315 }}} mi
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{{{ 116.6667 + 128.3315 = 244.9982 }}}
Now add the headstart of {{{ d[1] = 55 }}} mi
{{{ 244.9982 + 55 = 299.9982 }}}
close enough to {{{ 300  }}} mi
OK