This problem solving activity has an algebra focus.
Rose and Ron are training for the Olympic Games.
They start off swimming from different ends of the pool and when they reach the opposite end they immediately turn and keep swimming.
When they meet the second time, Ron is swimming to the right end.
At that moment the ratio of their distance from the left end to the right end is 3:2.
What is the ratio of Ron’s speed to Rose’s speed?
To solve this problem, students are likely to first draw a diagram. From the diagram, they may more readily be able to express the situation using an equation. This will enable them to find a solution. To be able to generate and use an equation in this way, is an important mathematical skill to develop.
Rose and Ron are training for the Olympic Games. They start off swimming from different ends of the pool and when they reach the opposite end they immediately turn and keep swimming.
When they meet the second time, Ron is swimming to the right end. At that moment the ratio of their distance from the left end to the right end is 3:2. What is the ratio of Ron’s speed to Rose’s speed?
This time, the ratio of the distance from the left side of the pool when they met the second time, to the distance from the right side of the pool when they met the first time is 6:5. What is the ratio of Ron’s speed to Rose’s speed this time?
Let the length of the pool be L. When they meet Ron has travelled L + 3/5L and Rose has travelled L + 2/5L. So the ratio of their speeds is
When they first meet Ron has swum 5 units and together Rose and Ron have swum the length of the pool, L units. When Rose and Ron next meet, together they have swum 3L units. But for every length that they swim together, Ron swims 5 units. So at their second meeting, Ron has swum 3 x 5 = 15 units.
But when they meet the second time, Ron has also swum L + 6 units. So 15 = L + 6, so L = 9.
Now we know that when Ron and Rose first meet them, Ron has swum 5 units and Rose L – 5, which is 9 – 5 = 4. So the ratio of Ron’s speed to Rose's speed is 5:4.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/olympic-training at 8:58pm on the 26th February 2024