June 2024
Problem of the Month

Colorado Temperature Change

Mr. P checks the temperature in Fort Collins, Colorado several times each day.   On one particular day, he noticed that:

(1) The temperature at 8:00 AM was twice the temperature at 5:00 AM.

(2) The temperature at noon was equal to the sum of the temperatures at 5 AM and 10 AM.

(3) The temperature at 3:00 PM was 44 degrees warmer than the temperature at 5:00 AM.

(4) The sum of the temperatures at 5 AM and noon was equal to the sum of the temperatures at 8 AM and 10 AM.

(5) The sum of the five temperature readings (at 5 AM, 8 AM, 10 AM, noon, and 3 PM) equaled 183 degrees.

(6) The noon temperature was two degrees less than four times the 5 AM temperature.

What were the temperatures at 5:00 AM, 8:00 AM, 10:00 AM, noon, and 3:00 PM?
All temperatures are integer values and are measured in Fahrenheit degrees.

Solution:

The temperatures for that day were:
5:00 AM:   13°
8:00 AM:  26°
10:00 AM:  37°
Noon:  50°
3:00 PM:  57°

In Colorado, we often see temperature swings of thirty to forty degrees or more in the same day.

The temperatures in the problem occurred on March 19, 2023.

Click here to see the high and low temperatures for each day in 2023

Click here to see the hourly temperature readings for March 19, 2023

Let A = temperature at 5:00 AM
Let B = temperature at 8:00 AM
Let C = temperature at 10:00 AM
Let D = temperature at Noon
Let E = temperature at 3:00 PM

Then we can set up five equations:
(1)   B = 2A
(2)   D = 4A - 2
(3)   E - A = 44
(4)   A + D = B + C
(5)   A + B + C + D + E = 183

We can substitute into equation #5:
A + (B + C) + D + E = 183
A + (A + D) + D + E = 183
2A + 2D + (44 + A) = 183
3A + 2D = 139
3A + 2(4A - 2) = 139
11A - 4 = 139
11A = 143
A = 13
Then substitute back in to get the values of B, C, D, and E.

Correctly solved by:

1. K. Sengupta	Calcutta, India
2. Kamal Lohia	Holy Angel School, Hisar, Haryana, India
3. Dr. Hari Kishan	D.N. College, Meerut, Uttar Pradesh, India
4. Seth Cohen	Concord, New Hampshire, USA
5. Davit Banana	Istanbul, Turkey
6. Ivy Joseph	Pune, Maharashtra, India
7. Eloise Michael	Smith Academy, Hatfield, Massachussetts, USA
8. Pam Slone	Thacker, West Virginia, USA
9. Marsha Boggs	Williamson, West Virginia, USA
10. Kelly Stubblefield	Mobile, Alabama, USA

Send any comments or questions to: David Pleacher