Reena climbs up 5 stairs Every second and then climb down 2 stairs over the next second how many seconds will she take to climb 60 stairs?
Answers
By the end of 39 seconds, Reena climbed 60 steps
Step-by-step explanation:
The given problem is a sequence of steps climbed by Reena which is a progression for every second.
Let the sequence of terms be a1, a2, a3, ……. Where a1, a2, .. are the steps climbed by Reena at the end of first, second, third second…..
At the end of 1st second, number of stairs climbed up = 5
a1 = 5
By 2nd second, number of stairs climbed down = 2 number of steps climbed up = 3
a2 = 3
By 3rd second, number of stairs climbed up = 3 + 5 = 8
a3 = 8
By 4th second number of stairs climbed down = 8 - 2 = 6
a4 = 6
The sequence is 5, 3, 8, 6, 11, 9, ………….
This is a sequence with no definite pattern but we can see that when the sequence is split into two subsequence, pattern can be observed as follows:
5, 8, 11, ……. And 3, 6, 9, ……..
These two subsequence are in AP with common difference 3
We need to find out when or at which second, the steps in the sequence reaches 60.
Observe the sequence as follows:
5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, ………
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, …….
So, by 1st second number of steps climbed = 5; 2nd second steps = 3; 3rd second steps = 8; and so on.
We can see that after 57 steps 62 is the next number of steps. As the steps crossed 60, no more stepping down of 2 steps. This happened in between 38th and 39th second.
So, by the end of 39 seconds, Reena climbed 60 steps.
Given data:
Reena climbs up 5 stairs Every second and then climb down 2 stairs over the next second.
To find:
The total time taken by Reena to climb 60 stairs.
Solution:
As for every second she climbs 5 stairs and in the next second she climbs down 2 stairs,
Total stairs she climbs in 2 seconds = 5 - 2 = 3 stairs.
Total number of steps climbed by Reena = 60 stairs
Therefore, time take by Reena to climb 60 stairs
= (60/3)(2) [As she takes 2 seconds to climb 3 stairs]
= 40 seconds
But, at 39th second, we know that she climbs 5 stairs making it 62, which means, she'll be out of the complete 60 stairs making it no need to climb down further.
So, Time taken by Reena to climb 60 stairs = 40 – 1 = 39 seconds
Therefore, the total minimum time taken by Reena to climb 60 stairs is 39 seconds.
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