Question 132449
I set up {{{d = r*t}}} for both trains
{{{f}}} = freight train
{{{e}}} = express train
(1) {{{d[e] = r[e]*t[e]}}}
and
(2) {{{d[f] = r[f]*t[f]}}}
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{{{t[e] = 3}}}
{{{t[f] = 3}}}
They both travel for 3 hrs
{{{d[e] + d[f] = 390}}}km
{{{d[f] = 390 - d[e]}}}
{{{r[f] = r[e] - 30}}} km/hr
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(1) {{{d[e] = r[e]*3}}}
(2) {{{390 - d[e] = (r[e] - 30)*3}}}
{{{390 - d[e] = 3*r[e] - 90}}}
{{{d[e] = 480 - 3*r[e]}}}
substitute this for {{{d[e]}}} in (1)
{{{3*r[e] = 480 - 3*r[e]}}}
{{{6*r[e] = 480}}}
{{{r[e] = 80}}} km/hr
{{{r[f] = r[e] - 30}}}
{{{r[f] = 80 - 30}}}
{{{r[f] = 50}}} km/hr
The freight train's speed is 50 km/hr
The express train's speed is 80 km/hr
check:
(1) {{{d[e] = r[e]*3}}}
{{{d[e] = 80*3}}}
{{{d[e] = 240 km}}}
(2) {{{390 - d[e] = (r[e] - 30)*3}}}
{{{390 - 240 = (80 - 30)*3}}}
{{{150 = 150}}}
OK