Question

On a cold February morning, the temperature of the radiator fluid in Stanley's car is Negative 18 degrees Fahrenheit. When the engine is running, the temperature of the fluid goes up 5.4 degrees Fahrenheit per minute. Approximately how long will it take before the radiator fluid temperature reaches 60 degrees Fahrenheit?

Answer 1

Approximately 15 minutes

Explanation:

Let us use the idea of progression to solve the problem

Using arithmetic progression formula

Let the initial temperature be the first term i.e a = - 18°F

Since the fluid goes up by 5.4°F after 1 minutes, we can take our common difference to be 5.4°F

Looking for how long it take before the radiator fluid temperature reaches 60°F will be equivalent to looking for the number of terms 'n' when the nth term Tn is 60

Using the formula for finding the nth term of an Arithmetic sequence as shown:

Tn = a+(n-1)d

Substitute the given parameters

60 = -18+(n-1)(5.4)

Open the parentheses

60 = -18+(5.4n-5.4)

60 = -18+5.4n-5.4

60 = 5.4n-23.4

5.4n = 60+23.4

5.4n = 83.4

n = 83.4/5.4

n = 15.4

n ≈ 15

Hence it will take approximately 15minutes before the radiator fluid temperature reaches 60°F