Help with a tricky maths question.
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Help with a tricky maths question.

[From: ] [author: ] [Date: 12-08-27] [Hit: ]
using this method he needs to take a total of 40 steps to climb the 20 stairs. when climbing the same stairs jonathan takes 2 steps back after every 3 steps forward but each of jonathans steps take half as long as Adams.What fraction of the time it took Adam to climb the stairs does it take Jonathan?Answer was said to be 1.Thanks-This is one of those annoying types of question which bear no relation to real life.The trap is,......
I find it hard to focus on questions like this. How would you approach questions like this and how was the answer worked out?!?!
When climbing a flight of 20 stairs Adam takes 2 steps back after every 5 steps forward. using this method he needs to take a total of 40 steps to climb the 20 stairs. when climbing the same stairs jonathan takes 2 steps back after every 3 steps forward but each of jonathan's steps take half as long as Adam's.
What fraction of the time it took Adam to climb the stairs does it take Jonathan?

Answer was said to be 1.1

Thanks

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This is one of those annoying types of question which bear no relation to real life.

The trap is, that you reach the 20th step halfway through a step up/down pair. Thus for Adam:
5,3, 8,6, 11.9, 14,12, 17,15, 20
There'll fancier methods to do it, but I just count on my fingers. 5,8,11,14,17,20. Six step up/down pairs less the final step down = 6(5+2)-2 = 40 steps.

For Jonathan, 3,1, 4,2, 5,3 ... 18,16, 19,17, 20. Thus, 3,4,5 ... 18,19,20. Eighteen step up/down pairs (yes I did count on my fingers) less the final step down = 18(3+2)-2 = 88 steps.

Jonathan takes 2 steps every time Adam takes 1. So Adam takes 44 steps during the time Jonathan takes 88.

44/40 = 1.1.
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