Question 182489
For 1st train:
(a) {{{d[1] = r[1]*t[1]}}}
For 2nd train:
(b) {{{d[2] = r[2]*t[2]}}}
given:
(c) {{{d[1] + d[2] = 500}}} mi
(d) {{{r[1] = 60}}} mi/hr
(e) {{{r[2] = 50}}} mi/hr
(f) {{{t[2] = t[1] - 1}}} hrs
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Subtract {{{d[1]}}} from both sides of (c),
{{{d[2] = 500 - d[1]}}}
Now rewrite (a) and (b)
For 1st train:
(a) {{{d[1] = 60*t[1]}}}
For 2nd train:
(b) {{{500 - d[1] = 50*(t[1] - 1)}}}
I have 2 equations and 2 unknowns, so it's solvable
(b) {{{500 - d[1] = 50*(t[1] - 1)}}}
(b) {{{-d[1] = 50t[1] - 50 - 500}}}
(b) {{{-d[1] = 50t[1] - 550}}}
Now add (a) and (b)
(a) {{{d[1] = 60*t[1]}}}
(b) {{{-d[1] = 50t[1] - 550}}}
{{{0 = 60t[1] + 50t[1] - 550}}}
{{{110t[1] = 550}}}
{{{t[1] = 5}}} hrs
This is the time it took the DC to Charlston train to meet the other
The problem wants the time for the Charlston to DC train
{{{t[2] = t[1] - 1}}}
{{{t[2] = 5 - 1}}}
{{{t[2] = 4}}} hrs answer
check answer:
(a) {{{d[1] = r[1]*t[1]}}}
(a) {{{d[1] = 60*5}}}
(a) {{{d[1] = 300}}}
and
(b) {{{d[2] = r[2]*t[2]}}}
(b) {{{d[2] = 50*4}}}
(b) {{{d[2] = 200}}}
(c) {{{d[1] + d[2] = 500}}} mi
(c) {{{300 + 200 = 500}}}
OK