Question 1026312
{{{ d = r*t }}}
{{{ t = d/r }}}
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Let {{{ d }}} = distance in miles traveled at 5 mi/hr
{{{ 9 - d }}} = distance in miles traveled at 6 mi/hr
Let {{{ t }}} = time in hrs spent traveling at 5 mi/hr
{{{ 1.6 - t }}} = time in hrs spent traveling at 6 mi/hr
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Equation for traveling at 5 mi/hr
(1) {{{ t = d/5 }}}
Equation for traveling at 6 mi/hr
(2) {{{ 1.6 - t = ( 9 - d ) / 6 }}}
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(2) {{{ 6*( 1.6 - t ) = 9 - d }}}
(2) {{{ 9.6 - 6t = 9 - d }}}
(2) {{{ 6t - d = .6 }}}
and
(1) {{{ d = 5t }}}
Plug this into (2)
(2) {{{ 6t - 5t = .6 }}}
(2) {{{ t = .6 }}}
and
(1) {{{ d = 5*.6 }}}
(1) {{{ d = 3 }}}
and 
{{{ 1.6 - t = 1.6 - .6 }}}
{{{ 1.6 - t = 1 }}}
At 5 mi/hr, athelete jogged for .6 hrs
At 6 mi/hr athelete jogged for 1 hr
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check:
(1) {{{ t = d/5 }}}
(1) {{{ .6 = 3/5 }}}
(1) {{{ 3 = 3 }}}
and
(2) {{{ 1.6 - t = ( 9 - d ) / 6 }}}
(2) {{{ 1.6 -.6 = ( 9 - 3 ) / 6 }}}
(2) {{{ 1 = 6/6 }}}
(2) {{{ 1 = 1 }}}
OK