To catch a Thief

[zenith20]

i have found this forum such a nice one, cause whenever i ask a question, it would be kindly answered by its Moderators

i have another puzzle from Shakuntala Devi:

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"To catch a Thief
some time back while in England I am across a case in a criminal court .A man was being acccused of having stolen certain valuable jewels and trying to run away with them,when he was caught by a smart police officer who overtook him.

In cross examination the lawyer for accused asked the police officer how he could catch up with the accused who was already 27 steps ahead of him, when he started to run after him.'yes sir' the officer replied,'he takes eight steps to every five of mine.'

'But then officer',interrogated the lawyer ,'how did you ever catch him,if that was the case?'

'That's easily explained sir,' replied the officer ,'i have got a longer stride....two steps of mine are equal to his five. so the number of steps I required were fewer than his, and this brought me to the spot where i captured him.'

A member of the jury, who was particularly good at quick calculations did some checking and figured out the number of steps the police officer must have taken.

Can u also find out how many steps the officer needed to catch up with the thief?"
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the solution:
The police officer took thirty steps. in the same time the thief took forty-eight, which added to his start oftwenty-seven, that means he took seventy-five steps. This distance would be exactly equal to thirty steps of the Police Officer.
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my problem:
i have understood the case, but the solution's not so clear for me. could you plz explain it more.
thank you in advance,
Zenith

 

[mmm4444bot]

Let y = the thief's steps while being chased

Let x = the officer's steps

When talking about the ratio of actual numbers of steps, the 27 thief steps are not included.

y/x = 8/5

When talking about the stride ratio, it seems that the 27 steps are included.

x/(y + 27) = 2/5

The solution to this system of two equations is x = 30 and y = 48.

Tricky interpretation.

 

[zenith20]

Dear mmm4444bot
thanks for your solution, but, any more detailed explanations?

 

[Deleted member 4993]

Dear mmm4444bot
thanks for your solution, but, any more detailed explanations?

Exactly which part is giving you troUble?

 

[zenith20]

Re:

When talking about the stride ratio, it seems that the 27 steps are included.

x/(y + 27) = 2/5

here's my problem, could you plz explain why 27 is included then?

 

[Deleted member 4993]

Re: Re:

When talking about the stride ratio, it seems that the 27 steps are included.

x/(y + 27) = 2/5

here's my problem, could you plz explain why 27 is included then?

The total number of steps the police officer would have to take to catch the thief - we need to add 27 here because to get to the position the thief was he would have to take 27 steps. Then the officer would have to take 'x' more steps to thiefs 'y' steps to cover the same distance.

 

[zenith20]

Thanks for your explanation Subhotosh Khan