Trains on two different routes stop at the same train station.
Trains on one route stop there every 9 minutes and trains on the other route stop there every 6 minutes.

Trains on both routes stop at the train station at midday. How many minute later will it be when trains on both routes next stop there at the same time?

Step 1 ：Given that trains on one route stop at the station every 9 minutes and trains on the other route stop there every 6 minutes, we need to find the least common multiple (LCM) of 9 and 6. The LCM of two numbers is the smallest number that is a multiple of both numbers.

Step 2 ：Let's denote the interval of the first train as \(train1_{interval}\) and the interval of the second train as \(train2_{interval}\). So, \(train1_{interval} = 9\) and \(train2_{interval} = 6\).

Step 3 ：We calculate the LCM of \(train1_{interval}\) and \(train2_{interval}\), which is 18.

Step 4 ：\(\boxed{18}\) minutes after midday, trains on both routes will stop at the station at the same time.