Question 178582
For the bus, I can write
(1) {{{d[b] = r[b]*t[b]}}}
For the train, I can write
(2) {{{d[t] = r[t]*t[t]}}}
They are starting at the same time. Suppose I have a stopwatch
and I am high above them in a blimp or baloon.
I start the stopwatch when they both start and I can actually
measure when they are 24 mi apart, and I'll stop the watch then.
Then I will know that the elapsed time for each will be the same, or
{{{t[b] = t[t]}}}, so I'll just call them both {{{t}}}
given:
{{{r[b] = 31}}} mi/hr
{{{r[t] = 39}}} mi/hr
So far, I have:
(1) {{{d[b] = 31t}}}
(2) {{{d[t] = 39t}}}
I want the train to be {{{24}}} mi ahead of the bus when I stop
the stopwatch, so I want
{{{d[t] = d[b] + 24}}}
Now I can write
(1) {{{d[b] = 31t}}}
(2) {{{d[b] + 24 = 39t}}}
Substitute {{{d[b]}}} in (1) for {{{d[b]}}} in (2)
{{{31t + 24 = 39t}}}
{{{8t = 24}}}
{{{t = 3}}} hrs 
In 3 hours, they will be 24 miles apart
check:
(1) {{{d[b] = 31t}}}
(2) {{{d[t] = 39t}}}
-----------
{{{d[b] = 31*3}}}
{{{d[b] = 93}}}
and
{{{d[t] = 39*3}}}
{{{d[t] = 117}}}
{{{117 - 93 = 24}}}
OK