To solve this problem, we need to break down the total distance that Barat walked and then find out how far he walked from his calculus class back to his dormitory.
First, let's list the distances he walked to each class:
- To the biology class: [tex]\(\frac{3}{30}\)[/tex] mile
- To the art class: [tex]\(\frac{3}{30}\)[/tex] mile
- To the calculus class: [tex]\(\frac{5}{30}\)[/tex] mile
Next, we need to compute the total distance walked to these classes.
1. Distance to biology class: [tex]\(\frac{3}{30}\)[/tex] mile
2. Distance to art class: [tex]\(\frac{3}{30}\)[/tex] mile
3. Distance to calculus class: [tex]\(\frac{5}{30}\)[/tex] mile
Total distance walked to the classes:
[tex]\[ \frac{3}{30} + \frac{3}{30} + \frac{5}{30} \][/tex]
Now, we add these fractions. Since they have the same denominator, we can directly add the numerators:
[tex]\[ \frac{3}{30} + \frac{3}{30} + \frac{5}{30} = \frac{3 + 3 + 5}{30} = \frac{11}{30} \][/tex]
So, the total distance walked to the classes is [tex]\(\frac{11}{30}\)[/tex] mile.
Barat walked a total of 1 mile. To find the distance he walked from his calculus class back to his dormitory, we subtract the distance walked to the classes from the total distance walked:
[tex]\[ 1 - \frac{11}{30} \][/tex]
To perform this subtraction, we convert the whole number 1 to a fraction with the same denominator:
[tex]\[ 1 = \frac{30}{30} \][/tex]
Now we subtract [tex]\(\frac{11}{30}\)[/tex] from [tex]\(\frac{30}{30}\)[/tex]:
[tex]\[ \frac{30}{30} - \frac{11}{30} = \frac{30 - 11}{30} = \frac{19}{30} \][/tex]
Thus, the distance Barat walked from his calculus class to his dormitory is [tex]\(\frac{19}{30}\)[/tex] mile.
