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: [tex]37.5^{\circ}[/tex]  or  [tex]37\dfrac{1}{2}^{\circ}[/tex] Step-by-step explanation:Given : The temperature of the liquid changed by [tex]-82\dfrac{1}{2}^{\circ}C[/tex] over [tex]2\dfrac{1}{5}[/tex] minutes.We can write [tex][tex]82\dfrac{1}{2}=\dfrac{82\times2+1}{2}=\dfrac{165}{2}[/tex][tex]2\dfrac{1}{5}=\dfrac{11}{5}[/tex]Now, the statement becomes ,The temperature of the liquid changed by [tex]-\dfrac{165}{2}^{\circ}C[/tex] over [tex]\dfrac{11}{5}[/tex] minutes.i.e. temperature changed in [tex]\dfrac{11}{5}[/tex] minutes =  [tex]-\dfrac{165}{2}^{\circ}C[/tex]Now, by Unitary method, The temperature changed in 1 minute =   [tex]\dfrac{165}{2}\times\dfrac{5}{11}^{\circ}C[/tex]⇒ The temperature changed in 1 minute = [tex]37.5^{\circ}[/tex] or  [tex]37\dfrac{1}{2}^{\circ}[/tex]