Old skool IQ type question?

Question

If Johnny goes from home to school at x miles per hour, and returns home from school at kx miles per hour, and he travels frpm 1 hour, what is the total distance covered?

Answer 1

Let D = distance between home and school.

Using the formula : distance = speed * time, we have :

From home to school : D = x * T1
From school to home : D = kx * T2

Therefore, x * T1 = kx * T2
Dividing through by x gives :
T1 = k * T2

We know that T1 + T2 = 1 (total time travelled)
Therefore, T2 = 1 - T1.

Substituting this into T1 = k * T2 gives :
T1 = k (1 - T1)

From this, we find that :
T1 = k / (k + 1)

Substituting into 'home to school equation' gives :
D = x * k / (k + 1)

Therefore total distance covered
= 2D
= 2 * x * k / (k + 1) miles.

Answer 2

Since he only travels for one hour (total, I am assuming):

total = kx + x = x(k + 1) miles