Problem requiring decisions

## Problem

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?

1. 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.

2. 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?

3. 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?

4. 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?

5. 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?

6. 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?

1. 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?