Sugary diversion
Weekly Problem 48 - 2008
An ant is crawling in a straight line when he bumps into a one centimetre cube of sugar.If he climbs over it before before continuing on his intended route, how much does the detour add to the length of his journey?
An ant is crawling in a straight line when he bumps into a one centimetre cube of sugar.If he climbs over it before before continuing on his intended route, how much does the detour add to the length of his journey?
Age
11 to 14
Challenge level
Problem
Image
An ant is crawling in a straight line from one corner of a table to the opposite corner when he bumps into a one centimetre cube of sugar.
Instead of crawling round it, or eating his way through it, he climbs straight up and over it before continuing on his intended route.
How much does the detour add to the length of his journey?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
The ant climbs up the cube (adding $1 \; \text{cm}$), walks across the top of the cube on the same path as he would have done if the cube wasn't there, then climbs back down to the table (adding another $1 \; \text{cm}$), so the total extra distance is $2 \; \text{cm}$ .