You may also like

problem icon

On the Road

Four vehicles travelled on a road with constant velocities. The car overtook the scooter at 12 o'clock, then met the bike at 14.00 and the motorcycle at 16.00. The motorcycle met the scooter at 17.00 then it overtook the bike at 18.00. At what time did the bike and the scooter meet?

problem icon

Pentagonal

Can you prove that the sum of the distances of any point inside a square from its sides is always equal (half the perimeter)? Can you prove it to be true for a rectangle or a hexagon?

problem icon

A Scale for the Solar System

The Earth is further from the Sun than Venus, but how much further? Twice as far? Ten times?

Speed-time Problems at the Olympics

Stage: 4 Challenge Level: Challenge Level:1

Why do this problem?

This task provides an engaging context for students to explore speed, distance and time problems. Some of the questions require students to make assumptions or find out extra information.

 

Possible approach

This worksheet contains all eight questions and could be distributed to students.

 
Here is a PowerPoint presentation with a separate slide for each question.
 
Here are some ways the questions in this problem could be used:
 
  1. Display one question at the start of a lesson, give students some time to work out their response, and then discuss as a class different ideas and methods.
     
  2. Give all eight questions out and invite students to work on them in pairs or small groups before bringing the class together to share their answers and debate any disagreements.
     
  3. Give out different questions to different pairs and then invite each pair to present their answer, with the rest of the class acting as critical friends insisting on clear reasoning.

There may be opportunities for cross-curricular links with P.E. where students may have collected their own data about their best times for 100 and 200m. It may be appropriate to adapt some of these questions and use students' own times.

 

It is important to be aware throughout that these questions are (deliberately!) not as 'precisely' stated as typical textbook questions. For example, the phrase 'If she had continued running ...' from lane 2 requires an assumption to be made before computation of an answer. There is no absolutely 'right' way to make these assumptions, although assumptions need to be made clearly. You might need to encourage or reassure the class that they are 'allowed' to make their own sensible assumptions on which to base their calculations if they are unused to working in this way. You might find that rich mathematical discussion emerges from the discussion of the modelling assumptions made on certain parts of the question.

 

Key questions

What assumptions do you need to make?
Is there any extra information you need to know?

 

Possible extension

The challenging task Speedo invites students to think about questions of speed, distance and time where acceleration plays a part.

 

Possible support

 
We assume students will use calculators when working on these questions. Inviting students to work together will allow them to support each other. Some of the questions could be worked on as a whole class and solution methods could be modelled on the board. The first four questions are similar in nature, and easier than the last four.
 
Place Your Orders might provide a suitable introductory activity.