Question 391974
For train A:
{{{d[A] = (r - 14)*t[A]}}}
For train B:
{{{d[B] = r*t[B]}}}
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given:
{{{d[A] = 190}}} mi
{{{d[B] = 260}}} mi
{{{t[A] = t[B]}}} hr
(since these times are equal, I'll call them both {{{t}}})
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I'll rewrite the equations:
(1) {{{190 = (r - 14)*t}}}
(2) {{{260 = r*t}}}
This is 2 equations and 2 unknowns, so it's solvable
(1) {{{190 = r*t - 14t}}}
(2) {{{260 = r*t}}}
Substitute (2) into (1):
(1) {{{190 = 260 - 14t}}}
{{{14t = 70}}}
{{{t = 5}}} hrs
Plug this back into (2):
{{{260 = r*5}}}
{{{r = 52}}} mi/hr
{{{r - 14 = 38}}} mi/hr
Train A's speed is 38 mi/hr
Train B's speed is 52 mi/hr