Final answer:
To find when the temperatures in Santa Fe and Minot will be the same, we set up an equation for the temperature change in each city. After setting up and solving the algebraic equation 86 - 3t = 56 + 2t, we find that the temperatures will be the same after 6 hours.
Step-by-step explanation:
To find when the temperature will be the same in Santa Fe, New Mexico and Minot, North Dakota, we can set up an algebraic equation representing the temperature change for each city. Let's use t to represent the time in hours after the initial observation. The temperature in Santa Fe is decreasing at a rate of 3 degrees per hour, and starts at 86 degrees, so the temperature at time t can be represented as 86 - 3t. Similarly, the temperature in Minot is increasing at a rate of 2 degrees per hour from an initial temperature of 56 degrees, which gives us 56 + 2t for its temperature at time t.
To find out when the temperatures are the same, we equate the two expressions:
86 - 3t = 56 + 2t
Now, we combine like terms and solve for t:
86 - 56 = 3t + 2t
30 = 5t
t = 30 / 5
t = 6
So, the temperatures will be the same after 6 hours.