SOLUTION: Hans and Peter form a team together. Hans is as old as Peter will be when Hans is twice as old as Peter was when Hans was half as old as the sum of their current ages. Peter is as

Hans is as old as Peter will be (x years from now)

H = P + x

(x years from now is) when Hans will be twice as old as Peter was (y years ago)

H + x = 2(P - y)

(y years ago was) when Hans was half as old as the sum of their current ages.

H - y = (H + P)

Peter is as old as Hans was (z years ago) 

P = H - z

(z years ago was) when Peter was half as old as he will become over ten years.


P - z = (P + 10)

We simplify the equations:

H = P + x                 or H - P - x = 0
H + x = 2(P - y)          or H + x = 2P - 2y  or H - 2P + x + 2y = 0
H - y = (H + P)         or 2H - 2y = H + P  or H - P - 2y = 0
P = H - z                 or -H + P + z = 0
P - z = (P + 10)        or 2P - 2z = P + 10 or P - 2z = 10

When simplified the five equations become

 H -  P - x           =  0
 H - 2P + x + 2y      =  0
 H -  P     - 2y      =  0
-H +  P          +  z =  0 
      P          - 2z = 10

That's 5 equations in 5 unknowns.  You can solve it by substitution
or by elimination or by matrix methods.  The solution is

H = 40, P = 30, x = 10, y = 5, z = 10

If you need help solving that 5×5 system of equations, post
again asking how.

Edwin