Answer:
Let's call the number of boxes delivered by the truck x. We know that the warehouse initially contains 55 boxes, and the truck delivers x boxes, so the total number of boxes in the warehouse after the delivery is 55 + x.
We also know that the workers unload the boxes at a constant rate, which we can express as a number of boxes per hour. Let's call this rate r. Since the workers unload boxes for 3.5 hours (from 12:00 p.m. to 3:30 p.m.), we can express the number of boxes unloaded as:
Number of boxes unloaded = r * 3.5
Therefore, the total number of boxes in the warehouse at 3:30 p.m. is:
55 + x - r * 3.5
We're told that this number is 90, so we can write the equation:
55 + x - r * 3.5 = 90
Simplifying this equation, we get:
x - r * 3.5 = 35
We're also told that the truck is empty at 8:30 p.m., which means that all the boxes it delivered have been unloaded by then. So the total number of boxes in the warehouse at 8:30 p.m. is:
55 + (x - r * 8)
where 8 is the number of hours between 12:00 p.m. and 8:00 p.m.
We can use the equation x - r * 3.5 = 35 to solve for x in terms of r:
x = 35 + r * 3.5
Substituting this into the equation for the total number of boxes at 8:30 p.m., we get:
55 + (35 + r * 3.5 - r * 8)
Simplifying this expression, we get:
55 - 35 + 28r
= 20 + 28r
Therefore, the warehouse contains 20 + 28r boxes at 8:30 p.m.