Reaction Forces - $2$ Concentrated Loads

Question

I have this question I've been attempting and need some guidance. I'm not exactly sure on how to go about this. I'll explain the image I've attached:

This is a gantry crane and it has two hoists along the beam which is $15m$ long. It has two vertical pillars at both ends. I have to assume the beam's weight is UDL (uniformly distributed load) of $1kN/m$ along the length of the beam. I've been told that both the hoists operate at $75kN$. Also, the beam is supposed to behave as a simply supported beam. I'm supposed to calculate the reaction forces applied on the beam by the vertical pillars at either end.

I've attached an image if it makes it more clearer, see it here:

Here's my attempt so far. What's my next step to take? Thank you

Answer 1

HINT

We have that

• vertical equilibrium $$R_L+R_R=75+75+15$$
• rotational equilibrium $$4.0\cdot 75+ 7.5\cdot 15 +10.0\cdot 75=15.0\cdot R_R$$