Fill in the dots with suitable values, and then answer the questions.

If you are working with a partner, you might wish to swap your version of the questions with them. Do you agree on your answers?

I first travel \(\dots\) miles at \(\quantity{x}{mph}\) and then travel the next \(\dots\) miles at \(\quantity{\dots}{mph}\). If my average speed is \(\quantity{\dots x}{ mph}\), what is \(x\)?

When thinking about a problem like this, it might help to try a simple case first. For example, what would happen if both distances are equal? What would a sensible answer be then? Perhaps try somewhat extreme numbers to check that your answer makes sense.

For more on average speeds, you could look at the Average speed resource.

I have an alloy made of two different metals. The first metal has density \(\quantity{\dots}{kg\,m^{-3}}\), while the second has density \(\quantity{\dots}{kg\,m^{-3}}\). The resulting alloy has density \(\quantity{\dots}{kg\,m^{-3}}\). What percentage of the alloy is the first metal?

I jog to the park at \(\quantity{\dots}{km/h}\) and then walk back along the same route at \(\quantity{\dots}{km/h}\). In total, I spent \(\dots\) hours jogging and walking there and back. How far did I jog?

I need to refill my empty paper stock cupboard. I can order two types of paper: regular paper is \(\quantity{x}{mm}\) thick per sheet, while SuperGrade paper is \(\quantity{\dots x}{mm}\) thick per sheet. I need to have \(\dots\) times as many regular sheets in my stock cupboard as SuperGrade ones, and the stock cupboard is \(\dots\) metres high. How many sheets of each will I be able to store?

A fish called Wanda and a shark called Jaws live peacefully together in a fish pond. Wanda could drink all of the water in the pond on her own in \(\dots\) hours, while Jaws would only take \(\dots\) hours to do the same. When they are together in the pond, how long would they take to drain it?

I have two chemicals, A and B, which both burn in oxygen. A glass chamber contains a certain amount of oxygen. There is just enough oxygen to completely burn either \(\dots\) grams of chemical A or a mixture of \(x\) grams of chemical A and \(\dots x\) grams of chemical B. How many grams of chemical B would completely burn in the chamber?

Countries A and B are adjacent. This table shows the birth rates, death rates and net migration rates (all given per 1000 population per year) for the two countries:

Country A Country B Birth rate \(\dots\) \(\dots\) Death rate \(\dots\) \(\dots\) Net migration rate \(\dots\) \(\dots\) The two countries agreed to unify into a single country, after which the net population growth rate of the unified country was \(\dots\) per 1000 population per year. What was the ratio of the populations of the two countries prior to the merger?

#### Further questions to consider

Is there more than one way to answer these questions?

What assumptions did you make in order to answer these questions? Are these reasonable?

Does your choice of values have any impact on how easy or hard it is to answer the questions?