A frog is climbing a greasy pole. The frog can climb 2 centimeters

Let's solve this by making a table

Time elapsed | height
1 hours | 4 cm
2 hours | 8 cm
REST (slide)
2.5 hours | 7 cm
3.5 hours | 11 cm
4.5 hours | 15 cm
REST (slide)
5 hours | 14 cm
6 hours | 18 cm
7 hours | 22 cm
REST (slide)
7.5 hours | 21 cm
8.5 hours | 25 cm
9.5 hours | 29 cm
Oops - we want too far.
We can see that the frog reaches a height of 28 cm BETWEEN 8.5 hours and 9.5 hours.
So, the correct answer must be C

Cheers,
Brent

It will climb 8m in 2hrs ---> then slips 1m in 0.5hr
Thus a total of 7m in 2.5hrs

7m ----> 2.5hr
21m ---> 7.5hr

Remaining 7m it will climb without slipping as distance left(7) is less then the total climb in single attempt(8)
Thus
8m ----> 2hr
7m ---->?
7*2 = x * 8
x = 1.75

Thus total time = 7.5+1.75 =9.25

In such case the caution is to think before the cycle of 2.5 hours end

In every 2.5 hours the Net Movement = 2*4 - 1 = 7 centimeter

i.e. (7*3=)21 cm will be climbed by him in 3*2.5 = 7.5 Hours

Now in 7.5 hours he is at height = 21
in 8 hours he is at height = 21+2 = 23
in 8.5 hours he is at height = 23+2 = 25
in 9 hours he is at height = 25+2 = 27
and in 9.5 hours he is at height = 27+2 = 29

i.e. He will be at 28 Centimeter height between 9 and 9.5 hour = 9.25 hour

Answer: option C

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As for the question, in every set of 2.5 hours, the frog's net movement will be 8 = 2*4 - 1 = 7 cm.

Thus in 2.5 * 3 hours, the frog will climb = 7*3 = 21 cm. Now the remaining 28-21 = 7 cm will be done by him in (7/8)*2 = 1.75 hours.

Thus the total time = 7.5+1.75 = 9.25 hours. C is the correct answer.

good one, tried to see the pattern first..
2h = climbs 8 cm
2.5h = 7.
thus, at 7.5h it will be at 21 cm (after the break)
8h=23cm
8.5h=25cm
9h=27cm

since it climbs 2cm every half hour, it means that 1 cm climbs in 0.25h.

thus, 9.25h is needed to climb 28cm

Another good question from veritas. It damaged my score since i made a careless mistake.
the frog reaches 28 after 2 rests. no need to add 30 min rest at the end as the frog is already at destination.

(1st interval) +2 (2nd interval) +2 (3rd interval) +2 (4th interval) +2 (5th interval) -1(while rest)
Effectively the frog climbs 7 cm in 2.5 hours.
Each interval is of half an hour only.

In 7.5 hours, the frog would have climbed 21 cms.
In the next 3 intervals, it would climb 6 cm.
The last cm climb will take it half the time to make the climb of 2 cm(15 mins)
Therefore the total time it takes the frog to climb 28 cm is 9 hours, 15 minutes or 9.25 hours(Option C)

In 2.5 hours, the frog can climb a total of 8 centimeters but will slip back 1 centimeter; thus, it will have covered a distance of 7 centimeters. We need to be careful not to just conclude that it will take 2.5 x 4 = 10 hours, because once the frog reaches the top, it will not rest and slip back again. Instead, we proceed as follows:

In 7.5 hours, the frog will be 21 centimeters high.

In 8 hours, the frog will be at 23 centimeters.

In 8.5 hours, the frog will be at 25 centimeters.

In 9 hours, the frog will be at 27 centimeters.

Since it takes 0.5 hours to climb 2 centimeters, it will take 0.25 hours to climb the final centimeter, and thus the frog will be on the top of the 28-centimeter pole in 9 + 0.25 = 9.25 hours.

Answer: C
_________________

1. For each 1/2 hour, the frog climbs 2 cm

2. After 2 hours, the frog take rest 1/2 hour and slips by 1 cm

=> For 2.5 hours, the frogs climb 7cm


=> Needs less than \(2.5 * (\frac{28}{7}) = 10\) hours

At after 9.5 hours => the frog already climbs 29 cm (the last 1/2 hour of the 10-hour period is the frog slipping 1cm)
At after 9.25 hours => the frog be climbs 28 cm (since for each 1/4 (=0.25) hour, the frog climbs 1 cm)

=> 9.25 hours

Answer C­