Question

test prep ricardo measured the temperature in the morning. the temperature was $-6\\, ^\circ\text{c}$. the temperature is increasing $1\frac{1}{2}\\, ^\circ\text{c}$ every hour. after how many hours will the temperature be at least $2\\, ^\circ\text{c}$?
show hints
\bigcirc less than 4 hours
\bigcirc $5\frac{1}{3}$ hours or more
\bigcirc more than $2\frac{1}{3}$ hours
\bigcirc less than $1\frac{1}{3}$ hours

Explanation:

Step1: Define the variable and inequality

Let \( h \) be the number of hours. The initial temperature is \(-6^\circ \text{C}\), and it increases by \( 1\frac{1}{2}^\circ \text{C}\) per hour. We want the temperature to be at least \( 2^\circ \text{C}\), so the inequality is \(-6 + 1\frac{1}{2}h \geq 2\).

Step2: Convert mixed number to improper fraction

\( 1\frac{1}{2}=\frac{3}{2} \), so the inequality becomes \(-6+\frac{3}{2}h \geq 2\).

Step3: Add 6 to both sides

\(\frac{3}{2}h \geq 2 + 6\), which simplifies to \(\frac{3}{2}h \geq 8\).

Step4: Solve for \( h \)

Multiply both sides by \(\frac{2}{3}\): \( h \geq 8\times\frac{2}{3}=\frac{16}{3}=5\frac{1}{3}\). So \( h \) is \( 5\frac{1}{3} \) hours or more.

Answer:

\( 5\frac{1}{3} \) hours or more (the third option: \( 5\frac{1}{3} \) hours or more)