Maths question help please

Hi, please could I have help on this question? If I make the right hand side positive and resolve as 25 cos alpha, why wouldn’t q be -15cos 2alpha, the ms says 15 cos 2 alpha?
Thank you!

It would help to say which part ... but if its i) and youre solving for t by
hz dist A + hz dist B = 72
then the distance B has travelled is positive.

yes sorry it was part i, but how would it be positive because if you resolve the arrow drawn, one would be pointing to the left and one arrow upwards? thanks

Which equation / part of the ms are you talking about? A distance is always positive, a displacement is signed so you may / may not ignore the sign depending on how its used.

when using s=ut, as highlighted in the ms, s is displacement so isn't the displacement -15cos 2alpha?

Sort of, but not necessarily? The usual suvat variables are signed so displacement, velocity, acceleration ... You could "derive" that equation by noting that the horizontal displacement of B relative to the origin of A is
72 - 15 cos(2 alpha) t
and you want the point where the two displacements are equal so
25 cos(alpha) t = 72 - 15 cos(2 alpha) t
....
But its probably more trouble than its worth to do it "properly".
As in the first reply, its probably more obvious to simply note that the horizontal motion for both is simply speed, distance, time (not signed) and you want the time when the horizontal distances sum to 72.

oh ok, i ended up doing it how you said but was confused with the signs, thank you

The thing with doing it "properly" so suvat, is to note that the displacements have to have the same origin if youre combining both motions. If you say sB = -15 ... and sA = 25 ... then there are two different origins. Adding 72 to sB means that they both now are relative to the initial point of A, but initial displacements like that are not part of the suvat equations, rather the initial displacement at t=0 is assumed to be s=0. In this case as there are two particles, you have to be more explicit about how you represent things.