This problem solving activity has a number focus.
These students are to sit an exam that begins at 9:30 pm sharp.
Which of them will get there in time for the start of the exam?
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.
This logic problem, involving positive and negative numbers in a practical situation, may challenge students and generate interesting discussion. Students need to possess knowledge of time to work successfully with this problem.
These students are to sit an exam that begins at 9:30 pm sharp. Which of them will get there in time for the start of the exam?
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.
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.
There are many ways of solving this problem. Here is one approach, using a table for each examinee.
Derek.
actual time | watch time | time Derek thinks it is |
9:30 | 9:45 | 9:35 |
9:25 | 9:40 | 9:30 |
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.
Marilyn.
actual time | watch time | time Marilyn thinks it is |
9:30 | 9:45 | 9:25 |
9:35 | 9:50 | 9:30 |
Marilyn will be 5 minutes late.
Sara, who will very very late.
actual time | watch time | time Sara thinks it is |
9:30 | 9:15 | 9:05 |
9:55 | 9:40 | 9:30 |
Tim. There are a lot of people coming late to this exam!
actual time | watch time | time Tim thinks it is |
9:30 | 9:15 | 9:25 |
9:35 | 9:20 | 9:30 |
The possibilities are:
Printed from https://nzmaths.co.nz/resource/time-problems at 2:56am on the 26th April 2024