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 6.9 degrees celsius per minute.
enter the number of minutes it will take the liquid and solid to reach the same temperature.

Explanation:

Step1: Define temperature functions

Let $t$ = time in minutes.
Liquid temperature: $T_L(t) = 16.9 - 2.3t$
Solid temperature: $T_S(t) = 30.7 - 6.9t$

Step2: Set temperatures equal

Set $T_L(t) = T_S(t)$:
$16.9 - 2.3t = 30.7 - 6.9t$

Step3: Rearrange to solve for t

Bring like terms together:
$6.9t - 2.3t = 30.7 - 16.9$
$4.6t = 13.8$

Step4: Calculate t value

Solve for $t$:
$t = \frac{13.8}{4.6}$

Answer:

3