Problem Statement: An insect climbs 2cm up a slippery rod in one second and slips 1cm over the next second. How many seconds will the insect take to reach the top of the rod 15cm high?

Solution:

To solve this problem, we need to calculate the number of seconds it will take the insect to reach the top of the rod by climbing 2cm up and slipping 1cm down. We can follow the steps given below:

Step 1: Calculate the net distance the insect climbs in each cycle

In each cycle, the insect climbs 2cm up and slips 1cm down. Therefore, the net distance the insect climbs in each cycle is 2cm - 1cm = 1cm.

Step 2: Calculate the number of cycles required to reach the top

To reach the top of the rod, the insect needs to climb a total distance of 15cm. Therefore, the number of cycles required to reach the top can be calculated as:

Number of cycles = Total distance to be climbed / Net distance climbed in each cycle
= 15cm / 1cm
= 15

Step 3: Calculate the total time taken to reach the top

In each cycle, the insect takes 2 seconds (1 second to climb up and 1 second to slip down). Therefore, the total time taken by the insect to climb 1cm is 2 seconds.

Since the insect needs to climb 15cm, it will take a total of 15 x 2 = 30 seconds to reach the top.

Answer: The insect will take 30 seconds to reach the top of the rod.