Problem of the Week Problem A and Solution Delivery Dilemma

Problem

At the beginning of the day, a delivery truck contains $$368$$ packages.
The driver of the truck is making deliveries to various office buildings in a city.

• Between $$9$$ a.m. and $$10$$ a.m., they deliver $$66$$ packages.

• Between $$10$$ a.m. and $$11$$ a.m., they deliver $$103$$ packages.

• Between $$11$$ a.m. and $$12$$ p.m., they deliver $$88$$ packages.

When the drivers returns to the depot for a lunch break, $$273$$ packages are added to the truck.

• Between $$1$$ p.m. and $$2$$ p.m., they deliver $$111$$ packages.

• Between $$2$$ p.m. and $$3$$ p.m., they deliver $$86$$ packages.

At $$4$$ p.m., they have $$99$$ packages left in the truck. How many packages did they deliver between $$3$$ p.m. and $$4$$ p.m.?

Solution

Since they start with $$368$$ packages in the truck, at $$10$$ a.m. they will have $$368 - 66 = 302$$ packages in the truck.
Then at $$11$$ a.m. they will have $$302 - 103 = 199$$ packages in the truck, and at $$12$$ p.m. they will have $$199 - 88 = 111$$ packages in the truck.

At lunch they add $$273$$ packages to the truck, so there are now $$111 + 273 = 384$$ packages in the truck.

Thus, in the afternoon, they start with $$384$$ packages in the truck.
Then at $$2$$ p.m. they will have $$384 - 111 = 273$$ packages in the truck, and at $$3$$ p.m. they will have $$273 - 86 = 187$$ packages in the truck.

Since there are $$99$$ packages on the truck at $$4$$ p.m., then there must have been $$187 - 99 = 88$$ packages delivered between $$3$$ p.m. and $$4$$ p.m.