Maths GCSE question

Hi, please could I have help on this question? I understand how to obtain the values but I don’t know how to work out the inequality? Thanks!

The velocity of Q is 2t-4 which is negative for 0<=t<2 and positive for t>2.

So you now need to consider the velocity of P and see where it's positive/negative. The velocity is a quadratic:

$v=3t^2-8t+5$

Try finding its roots and drawing a quick sketch to decide when it's positive/negative.

Then think about when both these velocities have the same sign.

Post your working if you get stuck.

Ahh yes the quadratic was positive and it works now. Where you mentioned that the velocities should have the same sign, is it because the particles are moving in the same direction? Thanks!

Yes that's right. Since you are told that both particles are moving on the same straight line, the sign of the velocity indicates the direction i.e. positive will be one way on the line and negative will be the opposite way. So for them to have the same direction, the signs of their velocities must be the same.