Question

Alexa conducted a scientific experiment. For a certain time, the temperature of a compound rose 3 1/2 degrees every start fraction 2/3 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 1

To find out how much the temperature of the compound rose in one hour, we start with the information given: the temperature rose \(3 \frac{1}{2}\) degrees every \( \frac{2}{3} \) of an hour.

First, we convert \(3 \frac{1}{2}\) degrees into an improper fraction:

\[
3 \frac{1}{2} = \frac{7}{2}
\]

Next, we need to determine how many \( \frac{2}{3} \) hours there are in one hour. We do this by dividing 1 hour by \( \frac{2}{3} \):

\[
1 \div \frac{2}{3} = 1 \times \frac{3}{2} = \frac{3}{2}
\]

This means there are \( \frac{3}{2} \) intervals of \( \frac{2}{3} \) hours in one hour.

Now we find the total temperature rise over one hour by multiplying the rise per interval by the number of intervals:

\[
\text{Total rise} = \left(\frac{7}{2}\right) \times \left(\frac{3}{2}\right)
\]

Next, we perform the multiplication:

\[
\frac{7}{2} \times \frac{3}{2} = \frac{7 \times 3}{2 \times 2} = \frac{21}{4}
\]

Finally, we convert \( \frac{21}{4} \) into a mixed number:

\[
\frac{21}{4} = 5 \frac{1}{4}
\]

Therefore, the total temperature rise of the compound in one hour is:

\[
\boxed{5 \frac{1}{4}}
\]