Equal gaps

In your book, Maths Mela (Chapter 5, Far and Near), Sheena and Jennifer are helping to organise a 3-km race. A 3-km race is 3,000 m long, because 1 km = 1,000 m.

Water stations are to be placed every 500 m. So the first water station is 500 m from the start, the next at 1,000 m, then 1,500 m, 2,000 m and 2,500 m. Each position is 500 m more than the one before. We keep adding 500 m: 500, 1,000, 1,500, 2,000, 2,500 …

Children stand every 300 m to show the runners the way. The first child is at 300 m, then 600 m, 900 m, 1,200 m, 1,500 m, 1,800 m, 2,100 m, 2,400 m, 2,700 m … Is there a child at 2,000 m? No: 2,000 m falls between 1,800 m and 2,100 m.

Is there a place with both a water station and a child? A water station is at 1,500 m, and a child is at 1,500 m too. So at 1,500 m the runners find both.

Flags are placed every 50 m: at 50 m, 100 m, 150 m, 200 m and so on. If one flag is at 1,250 m, the next is at 1,300 m.