A level further maths elastic spring and strings question

Hi, can someone help me understand the working out for this question, "a light elastic string of natural lenght 0.5m is streched between two points P and Q on a smooth horizontal table, the distance between P and Q is 0.75m, the modulus of elasticity is 30N. a particle of mass 0.5kg is attached to the midpoint of the string and the particle is pulled 0.1 m towards Q and released from rest. Find the speed of the particle as it passes through the midpoint of PQ. "

link to the worked solution, its question part b:
https://www.physicsandmathstutor.com/pdf-pages/?pdf=https%3A%2F%2Factiveteach-prod.resource.pearson-intl.com%2Fr00%2Fr0072%2Fr007257%2Fr00725775%2Fcurrent%2Falevelsb_fm1_ex3mix.pdf

We haven't done this topic in class but I've gone through the notes in the book and don't undertand how they calculated intial elastic potential energy, is the string modeled as two separate stings?

Thank you

The two halves are stretched different amounts so they have to be treated separately.

Oh I see, How come they are stretched by different amounts? (sorry if this is a stupid question)

No question is stupid. The particle is at the mid-point and that is pulled towards one end - it's a good idea to draw a diagram.