[Math] Word problem: Monkey climbing up a pole

algebra-precalculus

Problem edited since i missed a line from the problem,
A monkey wants to climb up a pole of 50 metre height. he first climbs up 1 m but he falls back by same height. Again he climbs up 2 m but he falls back by 1 m. Again he climbs up 3 m and falls back by 1 m. Again he climbs up 4 metre but falls back by 1 m. In this way he reaches top of the pole. If it is known that the monkey needs 10 secs for 1 metre in upward direction and 5 secs for 1 metre in downward direction. Then find the total time required by monkey to reach at the top of the pole.
Note that, when he will reach at the top he will not be slipped back hence find the total time required by this monkey to reach on the top of the pole.

I have solved this question and i have getting over 10 minutes as answer. But book's answer is 9 minutes 10 seconds. I am not getting why the answer differs.

solution:
(1,1) ,(2,1) ,(3,1),(4,1)the pair (x,y) where x=climbing interval and y=falling interval
now then…..
1st time =0m
2nd time =2-1=1m
3rd time =3-1=2m
4th time =4-1=3m
effective distance covered in 1 cycle=(0+1+2+3)=6m
total distance covered =climbing distance + falling distance…… (1)
for each cycle…..
climmbing distance =(1+2+3+4)=10
but ……
falling distance = (1+1+1+1)=4

total time for each cycle=time(climbing dist)+time(falling dist)
=10*10+4*5=120sec
this process repeats for 8 interval
hence 120*8=960 sec
after this i am not able to solve the problem

Best Answer

If $n$ is the number of times (and hence a total of $n$ meters) the monkey falls back, then when he reaches the top of the pole, the total distance he has moved upwards is $50+n$ meters (why? Hint: Instead of the monkey falling back, assume it was the pole that moved up by 1m).

Thus the time taken in seconds is $(50+n)\times 10 + n \times 5$.

Assuming the book answer is correct, we get

$$(50+n)\times 10 + n \times 5 = 550$$

i.e.

$$ 500 + 15n = 550$$

Thus

$$ n = 50/15 = 10/3$$

Thus the book answer you quote is wrong, irrespective of the steps of upward progression, if he falls back $1$m each time. The answer I get, assuming the upward progression as $1,2,4,8,16,32$ is less than $10$ minutes.

Are you sure you read the book answer correctly? Is it possible that you converted the answer given in seconds to minutes(and seconds) and might have made a mistake there?

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