Question

Alexa conducted a scientific experiment for a certain time the temperature of a compound rose 3 1/2 degrees every 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 determine how much the temperature of the compound rose in one hour, we start with the information provided: the temperature rises \(3 \frac{1}{2}\) degrees every \(\frac{2}{3}\) of an hour.

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

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

Now, we can find the rate of temperature change per hour. Since \(\frac{2}{3}\) of an hour is the time frame for which the temperature rises \( \frac{7}{2} \) degrees, we need to find out how many \( \frac{2}{3} \) time frames fit into 1 hour.

To find this, we divide 1 hour by \( \frac{2}{3} \):

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

This indicates that there are \( \frac{3}{2} \) intervals of \( \frac{2}{3} \) in 1 hour.

Next, we multiply the temperature rise in one interval by the number of intervals in one hour:

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

Now perform the multiplication:

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

Now, we can convert \( \frac{21}{4} \) to a mixed number:

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

Thus, the temperature of the compound rises by:

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

This is the simplest form of our answer.