Question

The height of a flagpole is 30 feet. Grease is applied to the pole. A monkey attempts to climb the pole. He climbs 3 feet for every second but slips down 2 feet in the next second. When will the monkey reach the top of the flag post?

Answer 1

Hint: Find the net height gained by the monkey each second to get the pattern that is required to solve the question. Try to find the time at which the monkey will reach ${{27}^{th}}$ feet. Consider this time as t seconds. Now, in the next second he will gain three feet and reach the top without slipping so the time (t + 1) seconds will be our answer.

Complete step by step solution:
Here we have been provided with a flag pole of height 30 feet and it is said that a monkey is trying to reach at the top of it according to the given conditions. We are asked to find the time at which he will reach the top of the pole.
Now, according to the question the monkey climbs three feet each second and falls the distance of 2 feet at the very next second. So let us try to examine a few seconds of the starting. At t = 1 second the monkey reaches 3 feet mark and at t = 2 seconds after slipping 2 feet he reaches at 1 feet mark. At t = 3 seconds he will reach 4 feet mark and at t = 4 seconds he will slip 2 feet and reach at 2 feet mark. Similarly, at t = 3 seconds he will be at 5 feet mark and then at t = 6 seconds he will slip at 3 feet mark.
When we observe this pattern we see that at every even second the monkey is at a mark of numerical value equal to half of that of the numerical value of time. So on carrying the process forward we will see that the monkey will be at 27 feet mark at t = 54 seconds. Now, in the very next second the monkey will gain 3 feet and reach the top of the pole before falling. So the time when he will reach the top will be given as (54 + 1) = 55 seconds.
Hence 55 seconds is our answer.

Note: You may get confused with the pattern of the advancement of the monkey and make the answer wrong by saying that he will take 60 seconds to get to the top as the half of 60 is 30, but this is where we need to think that after t = 54 seconds when he is at 27 feet mark he will climb 3 feet more to get to the top at t = 55 seconds. So he will not slip further as he will not climb further.