Quandaries and Queries

A worm is crawling to his home which is one meter away. The longer he crawls the weaker he gets and the less he can crawl the next day. If he crawls within 1/3000 of a meter of his home, he will find food. He must eat within twelve days. The first day he crawls 1/2 meter. The second day he crawls 1/4 meter. The third day he crawls 1/8 of meter. This pattern continues for twelve days. Make a Chart that shows the distance he has covered at the end of each day and the total he has covered at the end of each day. Does he make it to the Food in time?

This was given to my daughter in the 8 grade in middle school. I have tried to figure this out and the teacher says its a seventh grade problem. Help me teach my daughter to solve this.

Thank you Cindy

Hi Cindy,

My chart would start like this

 Day 1/2n Distance crawled n = 1 1/2 1/2 n = 2 1/4 1/2 + 1/4 = 3/4 n = 3 1/8 3/4 + 1/8 = 7/8 n = 4 1/16 7/8 + 1/16 = 15/16

Can you complete it? What is the distance remaining each day?

Penny

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