(a) Mia has her 40th birthday on 1st August and decides to set herself a fitness challenge to be archived before her birthday. She aims to run 10 km during April, 20 km during May, 30 km during June and 40 km during July. She starts with a run of 2.6 km in April which takes her 15 minutes. Calculate her average speed for this run, giving your answer in km/h.

(b) On July 31st, Mia still has 10.6 km left to run from her allocation for July. She would like to finish this run at an average speed of 13 km/h. Calculate the time this final run will take. Give your answer in minutes, correct to the nearest minute.

(c) Mia looks at the route for this final run on a map with a scale of 1 : 25 000. Part of the run goes through a country park and this section measures 15.7 cm on the map. Calculate the corresponding distance covered on the ground, giving your answer in kilometres correct to three significant figures.

(d) Mia's partner gives her membership of a running club for her birthday. She finds that she will be in the age category described as 'at least 35 but less than 50 years'. Let a represent the age of a runner, in years.

(i) Explain what the inequality a < 50 means in the practical context.

(ii) Draw a number line to illustrate the range of ages in Mia's age

category.

(iii) Write down a double inequality, using a, to describe this age category.