Question 1108737
Jim's headstart in miles is:
{{{ d[1] = 12*4 }}}
{{{ d[1] = 48 }}}
Start a stop watch when Sally leaves.
Let {{{ t }}} = time in hrs on stop watch when
Sally catches up with jim.
Let {{{ d }}} = distance in miles that Sally travels
during time {{{ t }}}
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Jim's equation:
(1) {{{ d - d[1] = 12t }}}
Sally's equation:
(2) {{{ d = 52t }}}
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(1) {{{ d - 48 = 12t }}}
(1) {{{ d = 12t + 48 }}}
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Plug (2) into (1)
(1) {{{ 52t = 12t + 48 }}}
(1) {{{ 40t = 48 }}}
(1) {{{ t = 6/5 }}}
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{{{ 6/5 = 1 + 1/5 }}}  hrs
{{{ (1/5)*60 = 12 }}} min
It will take 1 hr and 12 min for Sally to overtake Jim
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check:
(2) {{{ d = 52*(6/5) }}}
(2) {{{ d = 62.4 }}}
and
(1) {{{ d - 48 = 12*(6/5) }}}
(1) {{{ d = 48 + 14.4 }}}
(1) {{{ d = 2.4 }}}
OK