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A monkey is trying to reach the top of a tree. He climbs 3 feet in a minute but slides down by 1.5 feet after each climb. If he reaches the top of the tree in 58 minutes, then the maximum possible height of the tree is ____ feets.
- a)85.0
- b)87.3
- c)88.5
- d)90.1
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A monkey is trying to reach the top of a tree. He climbs 3 feet in a m...
You have to carefully observe the point that in the last minute, we DO NOT have to consider the sliding down of the monkey since the question states that the monkey reaches the top of the tree.Out of 58 minutes, the climb by monkey in 58th minute is 3 feet whereas for each of his earlier climbs, the monkey covers a net distance of 3-1.5=1.5 feet.We can work out the maximum possible height of the tree as 1.5×57+3=85.5+3=88.5 feet
Most Upvoted Answer
A monkey is trying to reach the top of a tree. He climbs 3 feet in a m...
Problem Analysis:
Let's break down the information given in the problem:
- The monkey climbs 3 feet in a minute.
- After each climb, the monkey slides down by 1.5 feet.
- The monkey reaches the top of the tree in 58 minutes.
We need to find the maximum possible height of the tree.
Solution:
To find the maximum possible height of the tree, we need to determine the number of climbs the monkey makes and the distance covered in those climbs.
Let's assume the maximum height of the tree is H feet.
Calculating the number of climbs:
- In each climb, the monkey covers a distance of 3 feet.
- After each climb, the monkey slides down by 1.5 feet.
- So, the net distance covered in each climb is 3 - 1.5 = 1.5 feet.
In 58 minutes, the monkey will make X climbs:
- X climbs * 1.5 feet climb distance = H feet
- X * 1.5 = H
Calculating the total distance covered:
In 58 minutes, the monkey spends X-1 minutes climbing and sliding down:
- (X-1) climbs * 3 feet climb distance = H feet
- (X-1) * 3 = H
Combining the equations:
We have two equations:
- X * 1.5 = H
- (X-1) * 3 = H
Simplifying the second equation:
- 3X - 3 = H
Substituting the value of H from the first equation into the second equation:
- 3X - 3 = X * 1.5
- 3X - 3 = 1.5X
- 1.5X = 3
- X = 2
Calculating the maximum height of the tree:
Substituting the value of X into the first equation:
- 2 * 1.5 = H
- H = 3
Therefore, the maximum possible height of the tree is 3 feet.
Final Answer:
The correct option is (C) 3 feet.
Let's break down the information given in the problem:
- The monkey climbs 3 feet in a minute.
- After each climb, the monkey slides down by 1.5 feet.
- The monkey reaches the top of the tree in 58 minutes.
We need to find the maximum possible height of the tree.
Solution:
To find the maximum possible height of the tree, we need to determine the number of climbs the monkey makes and the distance covered in those climbs.
Let's assume the maximum height of the tree is H feet.
Calculating the number of climbs:
- In each climb, the monkey covers a distance of 3 feet.
- After each climb, the monkey slides down by 1.5 feet.
- So, the net distance covered in each climb is 3 - 1.5 = 1.5 feet.
In 58 minutes, the monkey will make X climbs:
- X climbs * 1.5 feet climb distance = H feet
- X * 1.5 = H
Calculating the total distance covered:
In 58 minutes, the monkey spends X-1 minutes climbing and sliding down:
- (X-1) climbs * 3 feet climb distance = H feet
- (X-1) * 3 = H
Combining the equations:
We have two equations:
- X * 1.5 = H
- (X-1) * 3 = H
Simplifying the second equation:
- 3X - 3 = H
Substituting the value of H from the first equation into the second equation:
- 3X - 3 = X * 1.5
- 3X - 3 = 1.5X
- 1.5X = 3
- X = 2
Calculating the maximum height of the tree:
Substituting the value of X into the first equation:
- 2 * 1.5 = H
- H = 3
Therefore, the maximum possible height of the tree is 3 feet.
Final Answer:
The correct option is (C) 3 feet.
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Community Answer
A monkey is trying to reach the top of a tree. He climbs 3 feet in a m...
So in every minute, the net displacement of monkey is 1.5 m up. In 57 min , he moves up to 85.5 m
in the next minute,as he climbs up 3 m, he reaches the
top, so there is no need to slide down. so max height is 88.5m
in the next minute,as he climbs up 3 m, he reaches the
top, so there is no need to slide down. so max height is 88.5m
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