Question 193337
a  sketch  is  very  helpful  

ours  is  just  a  line
point  p  is  leftmost,  point  t  is  rightmost
r  is  midpoint
s  is  random  point  between  r  &  t
Given  PS=19,  and  qs-10
ps-qs=pq  from  sketch
19-10=9=pq,,,,,but  pq=qr(from  midpoint) therefore,,,qr=9
qs-qr=rs  from  sketch
10-9=1=rs,,,but  rt=18,,,therefore  st=18-1=17

check
p---9---q--9--r--1-s---17-----t
qs=10  ok
ps=19  ok