Question

lincoln conducted a scientific experiment. for a certain time, the temperature of a compound rose $3\frac{1}{2}$ degrees every $1\frac{3}{4}$ hours. what was the rate, in degrees per hour, that the temperature of the compound rose? 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 numbers to improper fractions

The temperature rise is \(3\frac{1}{2}\) degrees, which is \(\frac{3\times2 + 1}{2}=\frac{7}{2}\) degrees.
The time is \(1\frac{3}{4}\) hours, which is \(\frac{1\times4+3}{4}=\frac{7}{4}\) hours.

Step2: Calculate the rate (temperature per hour)

Rate is temperature divided by time, so we have \(\frac{7}{2}\div\frac{7}{4}\).
When dividing fractions, we multiply by the reciprocal: \(\frac{7}{2}\times\frac{4}{7}\).
The 7s cancel out, and \(\frac{4}{2} = 2\).

Answer:

\(2\)