If I travel to school on my bike at 18km/h, I get there 6 minutes late, but if I travel to school at20km/h, I get to school 4 minutes early. How far do I tr

Sure, let's solve this problem step by step.

1. First, let's convert the time difference into hours since the speed is given in km/h. 6 minutes late is 6/60 = 0.1 hours and 4 minutes early is 4/60 = 0.0667 hours.

2. Let's denote the distance to school as D (in km) and the time it should take to get to school as T (in hours).

3. From the problem, we can write down two equations based on the relationship speed = distance/time.

   For the first scenario (18km/h speed), we have: D = 18(T + 0.1)

   For the second scenario (20km/h speed), we have: D = 20(T - 0.0667)

4. Since both equations are equal to D, we can set them equal to each other and solve for T:

   18(T + 0.1) = 20(T - 0.0667)

   Simplifying this equation gives: T = 0.567 hours

5. Now, we can substitute T back into one of the original equations to find D. Let's use the first one:

   D = 18(T + 0.1) = 18(0.567 + 0.1) = 12 km

So, the distance to school is 12 km.