Question

Javier recorded the time (in hours) it took to finish his homework for 5 days: 2 12
, 3 13
, 2 34
, 3 12
, and 2 23
. What is the range of his homework times?

Answer 1

To find the range of Javier's homework times, we need to determine the maximum and minimum times from the recorded values.

First, let's convert the recorded times into decimal format for easier comparison.

1. Convert the times to hours in decimal form:
- \(2 \frac{1}{2}\) hours = \(2 + \frac{1}{2} = 2.5\) hours
- \(3 \frac{1}{3}\) hours = \(3 + \frac{1}{3} \approx 3.33\) hours (exactly \(3.3333...\))
- \(2 \frac{3}{4}\) hours = \(2 + \frac{3}{4} = 2.75\) hours
- \(3 \frac{1}{4}\) hours = \(3 + \frac{1}{4} = 3.25\) hours
- \(2 \frac{2}{3}\) hours = \(2 + \frac{2}{3} \approx 2.67\) hours (exactly \(2.6666...\))

Now, the converted times are:
- \(2.5\)
- \(3.33\)
- \(2.75\)
- \(3.25\)
- \(2.67\)

Next, identify the maximum and minimum values:
- Maximum: \(3.33\)
- Minimum: \(2.5\)

Finally, calculate the range:
\[
\text{Range} = \text{Maximum} - \text{Minimum} = 3.33 - 2.5 = 0.83
\]

Thus, the range of Javier's homework times is \(0.83\) hours.