Question 1053094
Find Jose's head start in miles
{{{ d[1] = 50*1 }}}
{{{ d[1] = 50 }}} mi head start
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Start a stop watch when Mary leaves. 
Let {{{ t }}}
= the time on the stop watch when Mary catches
up with Jose
Let {{{ d }}} = the distance Mary travel until she
catches Jose
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Mary's equation:
(1) {{{ d = 75t }}}
Jose's equation:
(2) {{{ d - 50 = 50t }}}
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Plug (1) into (2)
(2) {{{ 75t - 50 = 50t }}}
(2) {{{ 25t = 50 }}}
(2) {{{ t = 2 }}} hrs
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Jose traveled one hour for his head start and
then 2 more hours until Mary caught up with him
{{{ 1 + 2 = 3 }}}
So, Jose traveled 3 hrs until Mary caught up
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check:
(1) {{{ d = 75t }}}
(1) {{{ d = 75*2 }}}
(1) {{{ d = 150 }}} mi
and
(2) {{{ d - 50 = 50t }}}
(2) {{{ d - 50 = 50*2 }}}
(2) {{{ d = 50 + 100 }}}
(2) {{{ d = 150 }}} mi
OK