A caterpillar crawls up a pole high, starting from the ground. Each day it crawls up and each night it slides down . When will it first reach the top of the pole?
- AThe 70th day
- BThe 71st day
- CThe 72nd day
- DThe 75th day
Solution & Step-by-step Explanation
Net height gained by the caterpillar in one full day-and-night cycle:
On the final day, when the caterpillar climbs and reaches the exact top (), it will not slide down.
Subtract this final day's climb from the total height:
To cover this initial distance of at a net rate of , it will take exactly complete days.
On the next day ( day), it starts at and climbs :
Thus, it reaches the top for the first time on the day.
On the final day, when the caterpillar climbs and reaches the exact top (), it will not slide down.
Subtract this final day's climb from the total height:
To cover this initial distance of at a net rate of , it will take exactly complete days.
On the next day ( day), it starts at and climbs :
Thus, it reaches the top for the first time on the day.