Question 462486
Let {{{ d[1] }}} = distance faster train travels
Let {{{ d[2] }}} = distance slower train travels
given:
{{{ d[1] + d[2] = 400 }}}
faster train:
(1) {{{ d[1] = 110t }}}
slower train:
(2) {{{ d[2] = 90t }}}
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(a)
Add (1) and (2)
{{{ d[1] + d[2] = 110t + 90t }}}
{{{ 400 = 200t }}}
{{{ t = 2 }}} hrs
They will reach city c in 2 hours
(b)
(1) {{{ d[1] = 110t }}}
(1) {{{ d[1] = 110*2 }}}
(1) {{{ d[1] = 220 }}} mi
The faster train will travel 220 mi
check:
(2) {{{ d[2] = 90t }}}
(2) {{{ d[2] = 90*2 }}}
(2) {{{ d[2] = 180 }}} mi
{{{ 220 + 180 = 400 }}} mi
OK