Question 895049
Let {{{ t[1] }}} = time in hrs going
Let {{{ t[2] }}} = time in hrs coming back
Driving from Bedingfield to Portsmouth:
(1) {{{ d= 100t[1] }}}
Driving back:
(2) {{{ d = 75t[2] }}}
and, also:
(3) {{{ t[1] + t[2] = 3.5 }}}
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By substitution:
(1) {{{ 75t[2] = 100t[1] }}}
(1) {{{ t[1] = (3/4)*t[2] }}}
Substitute (1) into (3)
(3) {{{ (3/4)*t[2] + t[2] = 3.5 }}}
(3) {{{ 3t[2] + 4t[2] = 14 }}}
(3) {{{ 7t[2] = 14 }}}
(3) {{{ t[2] = 2 }}}
and
(3) {{{ t[1] = 3.5 - t[2] }}}
(3) {{{ t[1] = 3.5 - 2 }}}
(3) {{{ t[1] = 1.5 }}}
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(1) {{{ d= 100t[1] }}}
(1) {{{ d = 100*1.5 }}}
(1) {{{ d = 150 }}}
The distance between Bedingfield and Portsmouth
is 150 km
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check:
(2) {{{ d = 75t[2] }}}
(2) {{{ d = 75*2 }}}
(2) {{{ d = 150 }}}
OK