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