Question

A scientist is cooling a liquid at a steady rate. The temperature of the liquid changed by −82 1/2 °C over 2 1/5 minutes. What was the temperature change after 1 minute?

Answer 1

Answer: $37.5^{\circ}$  or  $37\dfrac{1}{2}^{\circ}$

Step-by-step explanation:

Given : The temperature of the liquid changed by $-82\dfrac{1}{2}^{\circ}C$ over $2\dfrac{1}{5}$ minutes.

We can write $[tex]82\dfrac{1}{2}=\dfrac{82\times2+1}{2}=\dfrac{165}{2}$

$2\dfrac{1}{5}=\dfrac{11}{5}$

Now, the statement becomes ,

The temperature of the liquid changed by $-\dfrac{165}{2}^{\circ}C$ over $\dfrac{11}{5}$ minutes.

i.e. temperature changed in $\dfrac{11}{5}$ minutes =  $-\dfrac{165}{2}^{\circ}C$

Now, by Unitary method,

The temperature changed in 1 minute =   $\dfrac{165}{2}\times\dfrac{5}{11}^{\circ}C$

⇒ The temperature changed in 1 minute = $37.5^{\circ}$ or  $37\dfrac{1}{2}^{\circ}$