Question 912941
First find train A's head start
{{{ d[1] = 100*1.5 }}}
{{{ d[1] = 150 }}} km
--------------------
Start a stopwatch when train B leaves
Let {{{ t  }}} = the time in hours it takes 
for B to catch A
Let {{{ d }}} = the distance that B travels 
until it catches A
--------------------
Train A's equation:
(1) {{{ d - 150 = 100t }}}
Train B's equation:
(2) {{{ d = 160t }}}
------------------
Substitute (2) into (1)
(1) {{{ 160t - 150 = 100t }}}
(1) {{{ 60t = 150 }}}
(1) {{{ t = 2.5 }}}
------------------
8:00 + {{{ 1.5 + 2.5 }}} = 12:00
Train B catches train A at 12:00
----------------------------
check:
(2) {{{ d = 160t }}}
(2) {{{ d = 160*2.5 }}}
(2) {{{ d = 400 }}}
and
(1) {{{ d - 150 = 100t }}}
(1) {{{ d - 150 = 100*2.5 }}}
(1) {{{ d = 250 + 150 }}}
(1) {{{ d = 400 }}}
OK