Time Problems

The Problem

We have a group of unfortunate people here. They all have an exam to do. It starts at 9:30 pm sharp. Which of them will get there in time for the start of the exam? Here’s the problem

Derek’s watch is 15 minutes fast but he thinks that it is 10 minutes fast.

Marilyn’s watch is 15 minutes fast but she thinks it is 20 minutes fast.

Sara’s watch is 15 minutes slow but she thinks it is 10 minutes fast.

Tim’s watch is 15 minutes slow but he thinks that it is 10 minutes slow.

Teaching sequence

1. Give the problem to the class to tackle in their groups. Allow discussion. When every group thinks they know the fate of one of our poor examinees, then have a reporting back session.
2. Take a vote on which of the four people get to the exam late. Then get students to give reasons for their choices.
3. Come to a consensus.
4. Let the students finish the problem. The quicker students could start on the Extension during this time.
5. Have another reporting back session.
6. Give students time to write up their answers.

Extension to the problem

Now there are other possibilities for people’s watches. They could be fast but they think they’re slow; they could be slow but they think they’re fast; they could be slow and their owners think that they are slower than that, and so on. Investigate the other possibilities and see what turns up.

Solution

There are lots of ways of doing this problem. We will use a table. First, Derek.

Here’s what we think about Derek. If it was 9:30, Derek’s watch would show 9:45 because it is 15 minutes fast. But Derek thinks it is 10 minutes fast. So he thinks that the actual time is 9:35. That gives the first row of the table.

But Derek wants to be at the exam at 9:30. So he will go there when he thinks that it is 9:30. But when he thinks that it is 9:30, his watch will be showing 9:40. However, the actual time then is 9:25. So Derek gets there in time.

Second, Marilyn. Look at the table.

Marilyn will be 5 minutes late.

Third, Sara. Look at the table again. Poor Sara; very late!

Fourth, Tim. There are a lot of people coming late to this exam!

Solution to the extension

The possibilities are:

1. watch fast by x; person thinks it is fast by y with y > x;
2. watch fast by x; person thinks it is fast by y with y < x;
3. watch fast by x; person thinks it is fast by y with y = x;
4. watch fast by x; person thinks it is slow by y with y > x;
5. watch fast by x; person thinks it is slow by y with y < x;
6. watch fast by x; person thinks it is slow by y with y = x;
7. watch slow by x; person thinks it is fast by y with y > x;
8. watch slow by x; person thinks it is fast by y with y < x;
9. watch slow by x; person thinks it is fast by y with y = x;
10. watch slow by x; person thinks it is slow by y with y > x;
11. watch slow by x; person thinks it is slow by y with y < x;
12. watch fast by x; person thinks it is slow by y with y = x.

What is your verdict for each of these situations? .