Question

in an experiment, the temperature of a liquid at 16.9 degrees celsius is decreasing at a rate of 2.3 degrees celsius per minute and the temperature of a solid at 30.7 degrees celsius is decreasing at a rate of 6.1 degrees celsius per minute. enter the number of minutes it will take the liquid and solid to reach the same temperature.

Explanation:

Step1: Set up the equation

Let $t$ be the number of minutes. The temperature of the liquid after $t$ minutes is $16.9 - 2.3t$, and the temperature of the solid after $t$ minutes is $30.7-6.1t$. We set them equal: $16.9 - 2.3t=30.7 - 6.1t$.

Step2: Move the terms with $t$ to one - side

Add $6.1t$ to both sides: $16.9 - 2.3t+6.1t=30.7 - 6.1t+6.1t$, which simplifies to $16.9 + 3.8t=30.7$.

Step3: Isolate the term with $t$

Subtract $16.9$ from both sides: $3.8t=30.7 - 16.9$. So, $3.8t = 13.8$.

Step4: Solve for $t$

Divide both sides by $3.8$: $t=\frac{13.8}{3.8}=\frac{138}{38}=\frac{69}{19}\approx 3.63$. But if we want a whole - number answer based on the context of the problem (assuming we are looking for an approximate integer value), we can round it. Since we are dealing with a real - world situation of temperature change over time, and we want to know when they will be approximately the same, we can say $t = 4$ (rounding up).

Answer:

4