The bar chart shows the distribution of students in a school according to the time they spend traveling from home to school. Fractions of a minute were disregarded; for example, if a student spends 40 minutes and 15 seconds on this journey, it is considered that the time spent is 40 minutes.

![](https://cdn.mathpix.com/cropped/2024_05_01_30c9a294a58a6e4b8190g-004.jpg?height=380&width=457&top_left_y=2097&top_left_x=1371)

Answer the following questions, justifying your answer.

(a) How many students spend less than 20 minutes to get to school?

(b) How many students are there in this school?

(c) How many students spend more than 40 minutes to get to school?

(d) Is it true that the majority of students spend more than 20 minutes to get to school?
The students of the school were divided into four distinct groups based on the time they spend traveling from home to school. Each of the four bars in the chart represents exactly one of these four groups, and each student in the school is in exactly one of these four groups.

(a) The students who spend less than 20 minutes on their commute from home to school are represented by the first bar, the tallest one, which reaches the mark of 90. Therefore, 90 students spend less than 20 minutes to get to school.

(b) The total number of students in the school is the sum of the numbers represented by the four bars, so the school has a total of $90+60+10+20=180$ students.

(c) The students who spend more than 40 minutes are divided into two groups: those who spend 41 to 60 minutes and those who spend more than 60 minutes, represented by the third and fourth bars, the two lowest ones, one reaching the mark of 10 and the other, the mark of 20. Therefore, the total number of students who spend more than 40 minutes to get to school is $10+20=30$ students.

(d) The students who spend between 20 and 40 minutes on their commute from home to school are represented by the second bar, which reaches the mark of 60. Together with the 30 students who spend more than 40 minutes (from the previous item), we have a total of $60+30=90$ students who spend more than 20 minutes to get to school. In the first item, we saw that 90 students spend less than 20 minutes to get to school, which is the same number as those who take more than 20 minutes, meaning that half of the students in the school take more than 20 minutes. We conclude that it is not true that the majority of students spend more than 20 minutes to get to school.