Point A, B , C and D lies on a straight line

This is a neat question!! 

This drawing shows the information from the problem:

1s + 5s   =   7t + 11t

6s   =   18t

1s   =   3t               (This is like a unit conversion!)

And...

    AB : BC : CD

=  1s : 7t - 1s : 11t                  Let's "convert"  s  into  t ,  using  1s  =  3t .

=  3t : 7t - 3t : 11t

=  3t : 4t : 11t

=  3 : 4 : 11

Haven't seen one like this before.....!!!

Since AB : BD  =  1 : 5   so...from A to D  there are  1 + 5 = 6 parts

And since AC : CD  = 7 : 11   and we can divide each 6th part into 7 + 11 = 18 more parts

So.....from A to D there are   6 * 18  =   108  equal parts

So  AB  =   [108 / 6] * 1  = 18  units

And BD  =  [108 / 6] * 5  = 90 units

And AC =  [ 108/ 18] * 7  = 42 units

And CD  =  [ 108 / 18] * 11 =   66 units

AB  = 18        

BC =  AC - AB =  42 - 18  =  24 units

CD  =  66 units

A           B            C                D

     18    +    24     +        66            =       108   

So   AB :   BC : CD    =    18 : 24 : 66  =    3 : 4 : 11

Thanks, hectictar......I was "feeling my way," here....but...I like your method better  !!

Thank you! I think I learned something new from this problem!