Question 876731
Time in hrs flying to the city:
(1) {{{ t[1] = d / 280 }}}
Time in hrs flying back:
(2) {{{ t[2] = d / 120 }}}
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(3) {{{ t[1] + t[2] = 4 }}}
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(1) {{{ d = 280t{1] }}}
(2) {{{ d = 120t[2] }}}
Subtract (2) from (1)
{{{ 280t[1] = 120t[2] }}}
{{{ t[2] = ( 7/3 )*t[1] }}}
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By substitution:
(3) {{{ t[1] + ( 7/3 )*t[1] = 4 }}}
(3) {{{ ( 10/3 )*t[1] = 4 }}}
(3) {{{ t[1] = (3/10)*4 }}}
(3) {{{ t[1] = 1.2 }}} hrs
and
{{{ t[2] = ( 7/3 )*t[1] }}}
{{{ t[2] = ( 7/3 )*(6/5) }}}
{{{ t[2] = 42/15 }}}
{{{ t[2] = 2.8 }}}
and
(1) {{{ d = 280t{1] }}}
(1) {{{ d = 280*1.2 }}}
(1) {{{ d = 336 }}}
check:
(2) {{{ d = 120t[2] }}}
(2) {{{ d = 120*2.8 }}}
(2) {{{ d = 336 }}}
The distance between the two airports
is 336 mi