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# Did You Find Out? Get the Answer to the Riddle of E-News Issue No. 4, September 2016

How long does it take a caterpillar to climb a tree?

On Monday morning at 7:00 a.m., a small caterpillar starts to climb up a tree at sunrise. Its goal is to reach the top of tree, which is 12.5 meters high, as the juiciest leaves are found there. The caterpillar crawls up 5 meters until sunset at 7 p.m. When it is dark, the little caterpillar sleeps in order to save energy for the next day. Every night when it is asleep, it slides down 1 meter.

On which day and at what time does the little caterpillar reach the leaves in the treetop when it is only crawling during daylight hours?

## Solution

The little caterpillar reaches the treetop on Wednesday afternoon at 5:48 p.m.

The caterpillar only crawls during daylight hours (from 7:00 a.m. to 7:00 p.m.). In these 12 hours, it covers a distance of 5 meters. The second half of the day, it sleeps while slipping down 1 meter. The small caterpillar crawls 4 meters up the tree within a 24 hours total (5-1). After two days, on Wednesday morning at 7:00 a.m., it is located 8 meters high in the tree. To finally reach the treetop in 12.5 meters, it still has to cover a distance of 4.5 meters. As the little caterpillar crawls 5 meters within 12 hours, it consequently needs 10 hours and 48 minutes for the remaining 4.5 meters (see calculation below). Finally, the caterpillar reaches its goal on Wednesday afternoon at 5:48 p.m.

Calculation

5 meters = 12 hours / :5
1 meter = 2.4 hours / x 4.5
4.5 meters = 10.8 hours ( = 10 hours and 48 minutes)

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