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?
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?
The Earth is further from the Sun than Venus, but how much further?
Twice as far? Ten times?
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.
These resources may be useful: Speed-Time Problems at the Olympics,
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.
What assumptions do you need to make?
Is there any extra information you need to know?
The challenging task Speedo invites students to think about questions of speed, distance and time where acceleration plays a part.