A physical education teacher trained with 5 students every day for 7 days. The average training time of the 5 students was 20.4 hours. The teacher trained for a total of 24 hours. Find the average training time of all people.

1. Problem Description

A physical education teacher trained with 5 students every day for 7 days. The average training time of the 5 students was 20.4 hours. The teacher trained for a total of 24 hours. Find the average training time of all people.

2. Solution Steps

First, calculate the total training time of the 5 students.

Total training time of students = number of students * average training time

$T_{students} = 5 \times 20.4 = 102$ hours.

Next, we calculate the average daily training time of the students.

Average daily training time of students = total training time of students / days in week

$DailyAvg_{students} = 102 / 7 \approx 14.57$ hours.

Next, we add the training time of the teacher to the student's training time to find the total training time of all people.

Total training time of all people = total training time of students + total training time of teacher

$T_{total} = T_{students} + T_{teacher} = 102 + 24 = 126$ hours.

Calculate the number of people. Number of people = number of students + 1 (teacher) = 5 + 1 = 6

Now we can calculate the average training time of all people.

Average training time of all people = total training time of all people / number of people

$Avg_{total} = \frac{T_{total}}{6} = \frac{126}{6} = 21$ hours

3. Final Answer

The average training time of all people is 21 hours.