Question 232405
When things are traveling in opposite directions
you can combine speeds, distances and times as if
it was just one thing moving at their combined speed
given:
{{{d = 270 + 360}}}
{{{d = 630}}} mi/hr
{{{v[1] = v[2] + 15}}}
Combined speed is {{{v + v + 15 = 2v + 15}}} (calling {{{V[2] = v}}}
--------------------
{{{630 = (2v + 15)*t}}}
{{{630 = 2vt + 15t}}}
Note that {{{vt}}} is the slower trains distance {{{vt = 270}}}
{{{630 = 2*270 + 15t}}}
{{{630 = 540 + 15t}}}
{{{15t = 90}}}
{{{t = 6}}} hrs
The speed of the faster train is:
{{{360/6 = 60}}} mi/hr
The slower tain's speed is:
{{{270/6 = 45}}} mi/hr
check answer:
{{{630 = (2v + 15)*t}}}
{{{630 = (2*45 + 15)*6}}}
{{{630 = 105*6}}}
{{{630 = 630}}}
OK