Question 395031
Time is the same for both examples.
For freight train:
{{{d = r*t}}}
(1) {{{250 = r[f]*t}}}
For passenger train:
(2) {{{310 = (r[f] + 12)*t}}}
There are 2 equation and 2 unknowns, so it's solvable
(2) {{{310 = r[f]*t + 12t}}
By substitution:
(2) {{{310 = 250 + 12t}}}
(2) {{{60 = 12t}}}
{{{t = 5}}} hrs
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From (1):
(1) {{{250 = r[f]*t}}}
{{{r[f] = 250/5}}}
{{{r[f] = 50}}} mi/hr
and,
{{{r[f] + 12 = 62}}}
The speed of the passenger train is 62 mi/hr
The speed of the freight train is 50 mi/hr
check:
(2) {{{310 = r[f]*t + 12t}}
{{{310 = 50*5 + 12*5}}}
{{{310 = 250 + 60}}}
{{{310 = 310}}}
OK