Question 269091
What is A's headstart?
{{{d = r*t}}}
{{{d = 40*4}}}
{{{d = 160}}} mi
Now you start a stopwatch. The start time and stop time
for both trains will be the same, or {{{t[a] = t[b]}}}
so call this time {{{t}}}
(1) {{{d[a] = r[a]*t}}}
(2) {{{d[b] = r[b]*t}}}
given:
{{{r[a] = 40}}}
{{{r[b] = 60}}}
So, now I have:
(1) {{{d[a] = 40t}}}
(2) {{{d[b] = 60t}}}
Train B has to make up the {{{160}}} mi headstart of train A, so
{{{d[b] = d[a] + 160}}}
So,  I have:
(1) {{{d[a] = 40t}}}
(2) {{{d[a] + 160 = 60t}}}
Substitute (1) into (2)
{{{40t + 160 = 60t}}}
{{{20t = 160}}}
{{{t = 8}}}
It takes 8 hrs for B to catch A
check:
(1) {{{d[a] = 40t}}}
{{{d[a] = 40*8}}}
{{{d[a] = 320}}}
(2) {{{d[b] = 60t}}}
{{{d[b] = 60*8}}}
{{{d[b] = 480}}}
{{{d[b] - d[a] = 480 - 320}}}
{{{480 - 320 = 160}}}
That was headstart of A