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 travel to school?

To solve this problem, we need to set up two equations based on the information given.

1. The first equation is based on the first scenario where the speed is 18km/h and the student arrives 6 minutes late. We can express the distance (d) as speed (s) times time (t). In this case, the speed is 18km/h and the time is t + 6/60 hours (since the student is 6 minutes late). So, the equation is: d = 18(t + 6/60).

2. The second equation is based on the second scenario where the speed is 20km/h and the student arrives 4 minutes early. Similarly, we can express the distance as speed times time. In this case, the speed is 20km/h and the time is t - 4/60 hours (since the student is 4 minutes early). So, the equation is: d = 20(t - 4/60).

Since the distance to school is the same in both scenarios, we can set the two equations equal to each other and solve for t:

18(t + 6/60) = 20(t - 4/60)

Solving this equation gives us t = 0.5 hours or 30 minutes. This is the time it should take to get to school on time.

Now that we have the time, we can substitute it into either of the original equations to find the distance to school. If we substitute it into the first equation, we get:

d = 18(t + 6/60) = 18(0.5 + 6/60) = 18(0.6) = 10.8 km

So, the distance to school is 10.8 km.