The time it takes Javier to go to school and his walking rate are inversely proportional. If it takes him 12 mins walking at 3 mph how long does it take if he walks at 4 mph?

t = k/r

12 = k/3
k = 36

t = 36/r

when r=4,

t=36/4 = 9 min

To solve this problem, we can use the concept of inverse proportionality.

Inverse proportionality states that if two quantities, in this case, the time taken and the walking rate, are inversely proportional, their product remains constant.

Let's denote the time taken as "t" in minutes and the walking rate as "r" in mph.

According to the given information, when Javier walks at 3 mph, it takes him 12 minutes. Therefore, we have:

t * r = constant

Substituting the given values, we have:

12 * 3 = k

So, k = 36.

Now, we can use the constant value to find the time taken when Javier walks at 4 mph:

t * 4 = 36

Divide both sides of the equation by 4:

t = 36 / 4

Simplifying, we find:

t = 9

Therefore, if Javier walks at 4 mph, it will take him 9 minutes to reach school.

To answer this question, we can use the concept of inverse proportion. In an inverse proportion, two variables are related in such a way that when one increases, the other decreases, and vice versa.

In this case, the time it takes Javier to go to school (let's call it "t") and his walking rate (let's call it "r") are inversely proportional. We know that when Javier walks at 3 mph, it takes him 12 minutes to reach school.

To solve the problem, we can use the equation for inverse proportion: t1 * r1 = t2 * r2, where t1 and r1 are the initial time and walking rate, and t2 and r2 are the new time and walking rate.

Substituting the given values:
t1 = 12 minutes (when Javier walks at 3 mph)
r1 = 3 mph
r2 = 4 mph (the new walking rate)

Let's solve for t2:
12 minutes * 3 mph = t2 * 4 mph

To find t2, let's simplify the equation by canceling out the units (minutes and mph):
36 = t2 * 4

Now, divide both sides of the equation by 4 to isolate t2:
36 / 4 = t2
9 = t2

Therefore, when Javier walks at 4 mph, it will take him 9 minutes to reach school.