Did you know that the deepest place on Earth is the Mariana Trench in the middle of the Pacific Ocean? It is 11,000 metres deep – that’s over 2,000 metres greater than the height of Mt. Everest!
Jing is a fearless scientist taking her submarine to the bottom of an ocean trench nearby the Mariana Trench. The first day she starts fast, going half the distance to the bottom of the trench. The second day she halves the remaining distance to the bottom. The third day she halves the remaining distance again, getting 1000 metres away from the bottom of the trench by the end of the day.
How deep is Jing’s oceanic trench?
Try making a vertical number line and divide it by two – this represents Jing’s progress on the first day. Take the bottom half and divide that by two – this represents the second day. Divide the resulting bottom half in two again, this represents the third day. Now where would you label the remaining 1,000 metres?
Let’s work backwards. On the third day we know two things: first, that Jing travelled half the distance to the bottom and second, that the remaining distance is 1,000 metres. That means Jing travelled 1,000 metres on the third day, and started that day 2,000 metres from the bottom.
Stepping back a day, she must have travelled 2,000 metres on the second day, leaving her 4,000 metres from the bottom. On the first day, she travelled 4,000 metres, making the total depth 8,000 metres!