Question 812408
What is the robber's head start?
{{{ d[1] = 13*(1/3) }}} ( converting 20 min to hrs )
{{{ d[1] = 13/3 }}}
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Start a stopwatch when the marshall leaves
Let {{{ t }}} = time on stopwatch when marshall
catches robber
Let {{{ d }}} = distance from Dodge City that
marshall catches robber
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robber's equation:
(1) {{{ d - 13/3 = 13t }}}
marshall's equation:
(2) {{{ d = 16t }}}
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(1) {{{ 3d - 13 = 39t }}}
(1) {{{ 3d = 39t + 13 }}}
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By substitution:
(1) {{{ 3*16t = 39t + 13 }}}
(1) {{{ 48t - 39t = 13 }}}
(1) {{{ 9t = 13 }}}
(1) {{{ t = 13/9 }}}
(1) {{{ t = 1 + 4/9 }}} hrs
(1) {{{ (4/9)*60 = 27 }}} min
The marshall catches the robber in 1 hr and 27 min