Let's say Dali's walking speed is x and his running speed is 3x.
In the morning, let's say the total distance is d. Therefore, Dali walks d/2 with speed x and runs d/2 with speed 3x. The time it takes for him to complete this distance is given by:
d/2x + d/2(3x) = 24
Simplifying this equation, we get:
d = 3x(8)
d = 24x
So, the total distance Dali covers in the morning is 24x.
After school, let's say the distance from school to home is d'. Therefore, Dali walks d'/2 with speed x and runs d'/2 with speed 3x. The time it takes for him to complete this distance is given by:
d'/2x + d'/2(3x) = ?
We don't know how much time it takes Dali to get home, so we'll leave the right-hand side of the equation blank for now.
Now, let's look at the ratios of Dali's walking and running speeds:
Walking speed : Running speed = x : 3x = 1 : 3
This means that for every 4 parts of the distance Dali covers, he walks one part and runs three parts. So, we can write:
d' = 4y, where y is the distance Dali walks
This also means that Dali spends one-fourth of the total time walking and three-fourths running. So, we can write:
d'/2x + d'/2(3x) = (1/4)t + (3/4)t, where t is the total time it takes Dali to get home
Simplifying this equation, we get:
2d' = 2t(x + 3x)
4y = 8tx
y = 2tx
Substituting this value of y in the equation d' = 4y, we get:
d' = 8tx
So, the total distance Dali covers in the afternoon is 8tx.
Now, we have two equations:
d = 24x
d' = 8tx
We need to simplify these equations further to find the value of t (the total time it takes Dali to get home).
From the first equation, we get:
x = d/24
Substituting this value of x in the second equation, we get:
d' = 8t(d/24)
d' = (1/3)dt
So, the total distance Dali covers in the afternoon is (1/3)dt.
Now, we can equate the two expressions we have for d':
d' = 8tx = (1/3)dt
Simplifying this equation, we get:
24x = t
Therefore, it takes Dali 24 minutes to get home.