Question

penelope conducted a scientific experiment. for a certain time, the temperature of a compound rose $1\frac{1}{2}$ degrees every $\frac{3}{4}$ of an hour. how much did the temperature of the compound rise in one hour? enter your answer as a whole number, proper fraction, or mixed number in simplest form.

answer attempt 1 out of 2

Explanation:

Step1: Convert mixed number to improper fraction

The temperature rise every \(\frac{3}{4}\) hour is \(1\frac{1}{2}\) degrees. Convert \(1\frac{1}{2}\) to an improper fraction: \(1\frac{1}{2}=\frac{3}{2}\).

Step2: Find the rate per hour

Let \(r\) be the rate (temperature rise per hour). We know that in \(\frac{3}{4}\) hour, the rise is \(\frac{3}{2}\) degrees. So we can set up the proportion: \(\frac{\frac{3}{2}\text{ degrees}}{\frac{3}{4}\text{ hour}} = r\). To divide by a fraction, multiply by its reciprocal: \(r=\frac{3}{2}\div\frac{3}{4}=\frac{3}{2}\times\frac{4}{3}\).

Step3: Simplify the multiplication

Simplify \(\frac{3}{2}\times\frac{4}{3}\). The 3s cancel out, and \(\frac{4}{2} = 2\). So \(r = 2\) degrees per hour.

Answer:

\(2\)