Calculating distance

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A drungard walks 5 steps forward and 3steps backward he takes 1 second for each step and each step is 1m long. In how many Seconds he would fall into a pit 13m ahead of him.

13 49 40 37

1 solution

Noel Lo
May 28, 2015

The time he falls into a pit 13 m ahead will be the FIRST time when he covers a displacement of 13 m. This first time should happen just after he makes 5 steps forward. The remaining 8 m would result from alternating series of 5 steps forward and 3 steps backward. Each of such series results in an overall displacement of $5-3 = 2$ metres. So we have $\frac{8}{2} = 4$ of such cycles. Each cycle takes $5+3 = 8$ seconds so 4 such cycles take $4 \times 8 = 32$ seconds. Adding this to 5 seconds needed for the last 5 steps we have $32+5 = \boxed{37}$ seconds in all.

But isn't this an assumption you make at the start of your argument ? That the drunk person will necessarily take all 5 steps before falling into the pit. This is nowhere hinted in the question (which simply asks how long will it take for the person to fall, given that he walks in this pattern). I could just as easily posit that he covers 12 m in this pattern (5 steps forward-3 backwards)and when he takes his next step ahead , he covers the last one meter and falls into the pit (never completing his pattern the last time round). If this were the case wouldn't the answer be 49 seconds. Since he takes 8 seconds to cover 2 meters. Hence he'll take 48 s to cover 12 m and when he takes one more step , he finally covers the 13th meter and finds the pit into which he falls .

utkarsh chawla - 5 years, 10 months ago

Calculating distance

1 solution

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