Question

weekly exercise
what is the difference between the longest time and the shortest time melissa spent exercising?
a \\(\frac{1}{2}\\) of an hour
b \\(\frac{3}{4}\\) of an hour
c \\(1\frac{1}{4}\\) of an hour
d 3 hours

Explanation:

Step1: Identify longest and shortest times

From the line plot, the shortest time is $\frac{1}{4}$ hour (where there are 3 X's) and the longest time is $1$ hour (one X at 1).

Step2: Calculate the difference

Subtract the shortest time from the longest time: $1 - \frac{1}{4} = \frac{4}{4} - \frac{1}{4} = \frac{3}{4}$? Wait, no, wait. Wait, looking again: Wait, the X at 1, X at $\frac{3}{4}$, $\frac{1}{2}$, and $\frac{1}{4}$. Wait, no, the longest time is 1 hour, shortest is $\frac{1}{4}$ hour. Wait, but let's check the options. Wait, maybe I misread. Wait, the X's: at $\frac{1}{4}$ (3 X's), $\frac{1}{2}$ (1 X), $\frac{3}{4}$ (1 X), 1 (1 X). So shortest time is $\frac{1}{4}$ hour, longest is 1 hour. Then difference is $1 - \frac{1}{4} = \frac{3}{4}$? But wait, option B is $\frac{3}{4}$? Wait, no, wait the options: A is $\frac{1}{2}$, B is $\frac{3}{4}$, C is $1\frac{1}{4}$, D is 3 hours. Wait, maybe I made a mistake. Wait, the longest time: the X at 1, so 1 hour. Shortest: $\frac{1}{4}$ hour. So $1 - \frac{1}{4} = \frac{3}{4}$ hour. So the answer should be B. Wait, but let's recheck. Wait, the line plot: the positions are 0, $\frac{1}{4}$, $\frac{1}{2}$, $\frac{3}{4}$, 1. The X's: at $\frac{1}{4}$: 3 X's, at $\frac{1}{2}$: 1 X, at $\frac{3}{4}$: 1 X, at 1: 1 X. So the times are $\frac{1}{4}$ (three times), $\frac{1}{2}$, $\frac{3}{4}$, 1. So the shortest time is $\frac{1}{4}$ hour, longest is 1 hour. Difference: $1 - \frac{1}{4} = \frac{3}{4}$ hour. So option B.

Answer:

B. $\frac{3}{4}$ of an hour