IMAT 2011 Q22 [Taxi Driver]

A taxi driver charges €1.00 per kilometre for the first 3 kilometres of a journey, and 70c per kilometre for the rest of the journey. I travel home from the train station by taxi. I pay the taxi driver €10.00 including a tip of 70c.

How far is my house from the station?

A. 9 kilometres

B. 10 kilometres

C. 12 kilometres

D. 13 kilometres

E. 14 kilometre

Some Quick Questions to ask yourself when doing this type of problem solving:

  • What is being asked? Underline the specifics in the question.
  • Analyse the data, is there anything we can eliminate immediately?
  • What information do I need to solve the question? Where can I find it?
  • How can I draw or use the graph to help me?

The best way to solve this question is to break it into steps. We have 3 main calculations we need to do here: The total cost minus the first 3 kilometers, the remainder of this - the tip of 70c, and finally whatever is left over divided by 0.70 to find the rest of the km travelled.

  1. €10 - €3 = €7

  2. €7-€0.70=€6.30

  3. €6.30/€0.70 per km = 9km

So we travelled 3km (cost of €3) + 9km (the remaining distance. Therefore the total distance travelled is 12km.

Final answer: C.