Practice run
Problem
Chandrika was practising a long distance run she was going to do
next week.
In the first 10 minutes she ran well over 2 kilometres.
In the second 10 minutes she jogged just half that distance.
In the third 10 minutes she walked just half as far.
In the fourth 10 minutes she dawdled only half of that and so
on.
Well, in theory at least, she would never have quite reached the end, but it happened that right at the end of a 10 minute stretch, exactly one metre from the finishing post, Chandrika tripped and fell forward over the line.
Getting Started
Remember that in the first $10$ minutes she ran well over $2$ kilometres.
What exact measurement do we know from the question?
How far had Chandrika to go when she fell?
How might you use a table to organise the information?
Student Solutions
Here are the figures that Rowena came up with:
"On practice run, the race was 4095 metres, and it takes two hours for Chandrika to do the long distance run.
First of all, I thought Chandrika ran 2000m, then jogged 1000m, then walked 500m, then 125, then 62.5m and I thought that there wouldn't be exactly one metre left.
If there was 1 metre left, she could have travelled 1m, 2m, 4m, 8m, 16m, 32m, 64 m, 128m, 256m, 512m, 1024m, 2048m.
If you add all these distances, you get 4095m. There are 12 lots of distance, 12 x10=120mins=2hours."
Daniel from Anglo-Chinese School, Singapore used the 'working backwards' method and got the same results except he included the final 10 minutes in the time.
Owen and Ian from Crofton Junior School, Kent built up a table. With a little rounding up of the numbers you see that it comes out very close to 4km in 2 hours.
| Minutes | Minutes so far | Distance in metres | Distance so far |
| 10 | 10 | 2 000.00 | 2 000.00 |
| 10 | 20 | 1 000.00 | 3 000.00 |
| 10 | 30 | 500.00 | 3 500.00 |
| 10 | 40 | 250.00 | 3 750.00 |
| 10 | 50 | 125.00 | 3 875.00 |
| 10 | 60 | 65.50 | 3 937.50 |
| 10 | 70 | 31.25 | 3 968.75 |
| 10 | 80 | 15.63 | 3 984.38 |
| 10 | 90 | 7.81 | 3 992.19 |
| 10 | 100 | 3.91 | 3 996.10 |
| 10 | 110 | 2.00 | 3 998.10 |
| 10 | 120 | 1.00 | 3 999.10 |
Teachers' Resources
Why do this problem?
This problem could be used when time, length and distance or doubling and halving are being introduced or discussed. It requires careful thinking to work out how the problem should be tackled so that doing it could lead to a useful classroom discussion.Possible approach
Key questions
How might you use a table to organise the information?