1. Jared regularly makes the 100 km journey to visit his family. The journey involves three separate stages:
•• A stage of 20 km that is travelled on small roads at a constant speed of 30 km/h.
•• A stage of 50 km that is travelled on the highway at a constant speed of 100 km/h.
•• A stage of 30 km that is travelled on standard roads at a constant speed of 40 km/h.

(a) How long does it normally take Paul to make this journey?

Last week there were roadworks on a section of the highway, and Paul was only able to travel at 60 km/h for the length of the roadworks. Paul’s journey last week took 6 minutes longer than usual.

(b) What was the length of the section of roadworks?

2. My local store sometimes runs offers on some of its products. There are three different types of offers that could be in place:

•• Buy a certain number of a particular product and get an extra one for half price.
•• A percentage discount (always a multiple of 5%) on one particular product.
•• A percentage discount (always a multiple of 5%) on purchases worth a total of more than $10.

The store only ever has one of these offers in place at any time.

Last week I bought:
3 cartons of orange juice for $4 each
1 loaf of bread for $3
5 packets of snacks for $1 each

This week I bought the same set of items, but only paid $18 even though the individual items still had the same price.

(a) There are two possible offers that could be applied to orange juice that would each explain this reduction in the total bill.
What are these two offers?

(b) What are the other two offers that could explain the reduction in the total bill?

(c) In order to work out which offer is in place this week, I am going to make another purchase.
What is the minimum that I must buy in order to be certain about which offer is in place?