Question 339026
Let beginning = {{{b}}}
Let middle = {{{m}}}
Let end = {{{e}}}
given:
(1) {{{b + m + e = 140}}} 
(2) {{{b = (1/6)*e}}}
(3) {{{m = (1/2)*e}}}
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There are 3 unknowns and 3 equations, so 
it should be solvable
Substitutute (2) in (1)
(1) {{{(1/6)*e + m + e = 140}}}
Substitute (3) in (1)
(1) {{{(1/6)*e + (1/2)*e + e = 140}}}
Multiply both sides by {{{6}}}
(1) {{{e + 3e + 6e = 840}}}
{{{10e = 840}}}
{{{e = 84}}}
And, from (2)
{{{b = (1/6)*84}}}
{{{b = 14}}}
From (3)
{{{m = (1/2)*84}}}
{{{m = 42}}}
The beginning is 14 min
The middle is 42 min
The end is 84 min
check:
(1) {{{b + m + e = 140}}}
{{{14 + 42 + 84 = 140}}}
{{{140 = 140}}}
(2) {{{b = (1/6)*e}}}
(2) {{{b = (1/6)*84}}}
{{{14 = 84/6}}}
{{{14 = 14}}}
(3) {{{m = (1/2)*e}}}
(3) {{{42 = (1/2)*84}}}
{{{42 = 42}}}
OK