You may recall the adventures of Midnight the cat and Myrtle the turtle from August 2022.
Well, Midnight is back, and I am assured that Myrtle is doing well somewhere in Australia.
In March 2024, the vet said that Midnight was 18 years old in human years.
You can determine Mr. P's age from the statement he gives when asked his age:
"I will be x + 34 years old in the year x-squared."
If the ratio of cat years to human years is 5:1, when were Mr. P and Midnight the same age (Mr. P in human years and Midnight in cat years)?
Solution:
In 2021, Mr. P and Midnight were both 75 years old.
From Mr. P's riddle, the year x2 must be 2025.
So x = 45.
That means that Mr. P will be 79 years old in 2025 (x + 34).
So, Mr. P turns 78 years old in 2024 when Midnight turns 90 years old (18 x 5).
Since Midnight gains 5 years for every year that Mr. P gains, you can construct the following table:
| Year | Mr. P | Midnight |
|---|---|---|
| 2024 | 78 | 90 |
| 2023 | 77 | 85 |
| 2022 | 76 | 80 |
| 2021 | 75 | 75 |
| 2020 | 74 | 70 |
If you want to get all mathy about it, you could also write two linear equations for the ages of Mr. P and Midnight and then determine where they intersect.
Let x = the year, and y equal the age (for Mr. P and for Midnight).
The equation for Mr. P's age can be found using the "point" (2024, 78) and the slope m = 1.
y - 78 = 1 (x - 2024) or y = x - 1946
The equation for Midnight's age can be found using the point (2024, 90) and slope = 5.
y - 90 = 5 (x - 2024) or y = 5x - 10030.
Now solving simultaneously, set the y-coordinates equal to find when they were the same age:
5x - 10030 = x - 1946
4x = 8084
So, x = 2021, the year that they are the same age.
Correctly solved by:
| 1. Kamal Lohia |
Holy Angel School, Hisar, Haryana, India |
| 2. K. Sengupta | Calcutta, India |
| 3. Colin (Yowie) Bowey | Beechworth, Victoria, Australia |
| 4. Kelly Stubblefield | Mobile, Alabama, USA |