Question 255405
Imagine you have a stopwatch and you start it when
the 2nd train leaves. You are all-knowing and powerful,
and can stop the stopwatch when the trains meet.
How far has the 1st train gone when you start the stopwatch?
{{{d = r*t}}}
{{{r = 60}}} mi/hr
{{{t = 1/2}}} hr
{{{d = 60*(1/2)}}}
{{{d = 30}}} mi
Now the 2 train will travel different distances but for the same time
on the stopwatch ({{{t[1] = t[2]}}})
For the 2nd train:
{{{d[2] = r[2]*t[2]}}}
{{{r[2] = 72}}} mi/hr
{{{d[2] = 72*t[2]}}}
The 1st train has {{{30}}} mi less to travel
{{{d[2] - 30 = 60*t[2]}}}
{{{d[2] = 60*t[2] + 30}}}
Use {{{d[2]}}} in the 1st equation for {{{d[2]}}} in the 2nd equation
{{{72*t[2] = 60*t[2] + 30}}}
{{{12*t[2] = 30}}}
{{{t[2] = 2.5}}} hrs
It will take the passenger train 2.5 hrs to catch the freight train
check:
The 1st train has traveled for {{{2.5 + .5 = 3}}} hrs
{{{d[1] = 60*3}}} mi
{{{d[1] = 180}}} mi
And the 2nd train's distance is
{{{d[2] = 72*2.5}}}
{{{d[2] = 180}}} mi
These are the TOTAL distances the trains must travel
and they are equal as they must be when they meet