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Question Number 112809 by Aina Samuel Temidayo last updated on 09/Sep/20

Answered by 1549442205PVT last updated on 11/Sep/20

Suppose the perimeter of race track is S then the time they meet from the start is (S/((9+8)))(s)=(S/(17))(s) The length of path two athlietes traveled from the start until they meet first time at A in turn equal to m.S and n.S respectively.Since the time and velocity are both proportional quantities,we have:((mS)/8)=((nS)/9)(m,n∈N) ⇔(n/m)=(9/8)⇔n=9,m=8.That means when they first time meet at A athliete moving with velocity 9m/s traveled the path equal to 9S(m) and athliete moving with velocity 8m/s traveled the path equal to 8S(m) and thus,the time each of them traveled in the time equal to S(s) Since the time required for a meeting of two persons is (S/(17))(s),number of times they met excluding the start and finish equal to S:(S/(17))−1=16(times) Answer:T hey met 16 times from the start at A untill they meet first time at A again excluding the start and finish

$$\mathrm{Suppose}\:\mathrm{the}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{race}\:\mathrm{track}\:\mathrm{is}\:\mathrm{S} \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{time}\:\mathrm{they}\:\mathrm{meet}\:\mathrm{from}\:\:\mathrm{the} \\ $$$$\mathrm{start}\:\mathrm{is}\:\frac{\mathrm{S}}{\left(\mathrm{9}+\mathrm{8}\right)}\left(\mathrm{s}\right)=\frac{\mathrm{S}}{\mathrm{17}}\left(\mathrm{s}\right) \\ $$$$\mathrm{The}\:\mathrm{length}\:\mathrm{of}\:\mathrm{path}\:\mathrm{two}\:\mathrm{athlietes} \\ $$$$\mathrm{traveled}\:\mathrm{from}\:\:\mathrm{the}\:\mathrm{start}\:\mathrm{until}\:\mathrm{they}\: \\ $$$$\mathrm{meet}\:\mathrm{first}\:\mathrm{time}\:\:\mathrm{at}\:\mathrm{A}\:\mathrm{in}\:\mathrm{turn}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\mathrm{m}.\mathrm{S}\:\mathrm{and}\:\mathrm{n}.\mathrm{S}\:\mathrm{respectively}.\mathrm{Since}\:\mathrm{the} \\ $$$$\mathrm{time}\:\mathrm{and}\:\mathrm{velocity}\:\mathrm{are}\:\mathrm{both}\:\mathrm{proportional} \\ $$$$\mathrm{quantities},\mathrm{we}\:\mathrm{have}:\frac{\mathrm{mS}}{\mathrm{8}}=\frac{\mathrm{nS}}{\mathrm{9}}\left(\mathrm{m},\mathrm{n}\in\mathrm{N}\right) \\ $$$$\Leftrightarrow\frac{\mathrm{n}}{\mathrm{m}}=\frac{\mathrm{9}}{\mathrm{8}}\Leftrightarrow\mathrm{n}=\mathrm{9},\mathrm{m}=\mathrm{8}.\mathrm{That}\:\mathrm{means}\: \\ $$$$\mathrm{when}\:\mathrm{they}\:\mathrm{first}\:\mathrm{time}\:\mathrm{meet}\:\mathrm{at}\:\mathrm{A}\: \\ $$$$\mathrm{athliete}\:\mathrm{moving}\:\mathrm{with}\:\mathrm{velocity}\:\mathrm{9m}/\mathrm{s} \\ $$$$\mathrm{traveled}\:\mathrm{the}\:\mathrm{path}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{9S}\left(\mathrm{m}\right)\:\mathrm{and} \\ $$$$\mathrm{athliete}\:\mathrm{moving}\:\mathrm{with}\:\mathrm{velocity}\:\mathrm{8m}/\mathrm{s} \\ $$$$\mathrm{traveled}\:\mathrm{the}\:\mathrm{path}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{8S}\left(\mathrm{m}\right) \\ $$$$\mathrm{and}\:\mathrm{thus},\mathrm{the}\:\mathrm{time}\:\mathrm{each}\:\mathrm{of}\:\mathrm{them} \\ $$$$\mathrm{traveled}\:\mathrm{in}\:\mathrm{the}\:\mathrm{time}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{S}\left(\mathrm{s}\right) \\ $$$$\mathrm{Since}\:\mathrm{the}\:\mathrm{time}\:\mathrm{required}\:\mathrm{for}\:\mathrm{a}\:\mathrm{meeting}\: \\ $$$$\mathrm{of}\:\mathrm{two}\:\mathrm{persons}\:\mathrm{is}\:\frac{\mathrm{S}}{\mathrm{17}}\left(\mathrm{s}\right),\mathrm{number}\:\mathrm{of}\:\mathrm{times}\: \\ $$$$\mathrm{they}\:\mathrm{met}\:\mathrm{excluding}\:\mathrm{the}\:\mathrm{start}\:\mathrm{and}\:\mathrm{finish} \\ $$$$\mathrm{equal}\:\mathrm{to}\:\mathrm{S}:\frac{\mathrm{S}}{\mathrm{17}}−\mathrm{1}=\mathrm{16}\left(\mathrm{times}\right) \\ $$$$\boldsymbol{\mathrm{Answer}}:\boldsymbol{\mathrm{T}}\:\boldsymbol{\mathrm{hey}}\:\boldsymbol{\mathrm{met}}\:\mathrm{16}\:\boldsymbol{\mathrm{times}}\:\boldsymbol{\mathrm{from}} \\ $$$$\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{start}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{A}}\:\boldsymbol{\mathrm{untill}}\:\boldsymbol{\mathrm{they}}\:\boldsymbol{\mathrm{meet}}\:\boldsymbol{\mathrm{first}}\: \\ $$$$\boldsymbol{\mathrm{time}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{A}}\:\boldsymbol{\mathrm{again}}\:\boldsymbol{\mathrm{excluding}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{start}} \\ $$$$\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{finish}} \\ $$

Commented by Aina Samuel Temidayo last updated on 10/Sep/20

This is not part of the options I have here. Please check your solution again. Thanks.

$$\mathrm{This}\:\mathrm{is}\:\mathrm{not}\:\mathrm{part}\:\mathrm{of}\:\mathrm{the}\:\mathrm{options}\:\mathrm{I}\:\mathrm{have} \\ $$$$\mathrm{here}.\:\mathrm{Please}\:\mathrm{check}\:\mathrm{your}\:\mathrm{solution} \\ $$$$\mathrm{again}.\:\mathrm{Thanks}. \\ $$

Commented by 1549442205PVT last updated on 10/Sep/20

I don′t understand what you want say?Perhaps,it should be corrected as above.Thank you

$$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{understand}\:\mathrm{what}\:\mathrm{you}\:\mathrm{want} \\ $$$$\mathrm{say}?\mathrm{Perhaps},\mathrm{it}\:\mathrm{should}\:\mathrm{be}\:\mathrm{corrected} \\ $$$$\mathrm{as}\:\mathrm{above}.\mathrm{Thank}\:\mathrm{you} \\ $$

Commented by Aina Samuel Temidayo last updated on 10/Sep/20

The question is an objective question, there are four options; one of which is the answer. So, I′m trying to say that 18 or 19 is not part of the 4 options. ⇒ 18 or 19 cannot be the answer.

$$\mathrm{The}\:\mathrm{question}\:\mathrm{is}\:\mathrm{an}\:\mathrm{objective}\:\mathrm{question}, \\ $$$$\mathrm{there}\:\mathrm{are}\:\mathrm{four}\:\mathrm{options};\:\mathrm{one}\:\mathrm{of}\:\mathrm{which} \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{answer}.\:\mathrm{So},\:\mathrm{I}'\mathrm{m}\:\mathrm{trying}\:\mathrm{to}\:\mathrm{say} \\ $$$$\mathrm{that}\:\mathrm{18}\:\mathrm{or}\:\mathrm{19}\:\mathrm{is}\:\mathrm{not}\:\mathrm{part}\:\mathrm{of}\:\mathrm{the}\:\mathrm{4} \\ $$$$\mathrm{options}.\:\Rightarrow\:\mathrm{18}\:\mathrm{or}\:\mathrm{19}\:\mathrm{cannot}\:\mathrm{be}\:\mathrm{the} \\ $$$$\mathrm{answer}. \\ $$

Commented by 1549442205PVT last updated on 11/Sep/20

I think I answered correctly requirement of question.From the start untill they meet first time at A then they met 17 times and last times at A Hence if excluding the start then they met total 17+1=18 times

$$\mathrm{I}\:\mathrm{think}\:\mathrm{I}\:\mathrm{answered}\:\mathrm{correctly} \\ $$$$\mathrm{requirement}\:\mathrm{of}\:\mathrm{question}.\mathrm{From}\:\mathrm{the}\: \\ $$$$\:\mathrm{start}\:\mathrm{untill}\:\mathrm{they}\:\mathrm{meet}\:\mathrm{first}\:\mathrm{time}\:\mathrm{at} \\ $$$$\mathrm{A}\:\mathrm{then}\:\mathrm{they}\:\mathrm{met}\:\mathrm{17}\:\mathrm{times}\:\mathrm{and}\:\mathrm{last} \\ $$$$\mathrm{times}\:\mathrm{at}\:\mathrm{A}\:\mathrm{Hence}\:\mathrm{if}\:\mathrm{excluding}\:\mathrm{the}\:\mathrm{start} \\ $$$$\mathrm{then}\:\mathrm{they}\:\mathrm{met}\:\mathrm{total}\:\mathrm{17}+\mathrm{1}=\mathrm{18}\:\mathrm{times} \\ $$

Commented by Aina Samuel Temidayo last updated on 11/Sep/20

Well, 17 is part of the options.

$$\mathrm{Well},\:\mathrm{17}\:\mathrm{is}\:\mathrm{part}\:\mathrm{of}\:\mathrm{the}\:\mathrm{options}. \\ $$

Commented by 1549442205PVT last updated on 11/Sep/20

You don′t note last parr of question?

$$\mathrm{You}\:\mathrm{don}'\mathrm{t}\:\mathrm{note}\:\mathrm{last}\:\mathrm{parr}\:\mathrm{of}\:\mathrm{question}? \\ $$

Commented by Aina Samuel Temidayo last updated on 11/Sep/20

I don′t really understand you.

$$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{really}\:\mathrm{understand}\:\mathrm{you}. \\ $$

Commented by 1549442205PVT last updated on 11/Sep/20

Excuse me .It need must be 17−1=16 I think 16 is correct answer because of last meeting time at A need must be excluded(i mistaked“ including ”and “excluding ”in English)

$$\mathrm{Excuse}\:\mathrm{me}\:.\mathrm{It}\:\mathrm{need}\:\mathrm{must}\:\mathrm{be}\:\mathrm{17}−\mathrm{1}=\mathrm{16} \\ $$$$\mathrm{I}\:\mathrm{think}\:\mathrm{16}\:\mathrm{is}\:\mathrm{correct}\:\mathrm{answer}\:\mathrm{because}\:\mathrm{of} \\ $$$$\mathrm{last}\:\mathrm{meeting}\:\:\mathrm{time}\:\mathrm{at}\:\mathrm{A}\:\mathrm{need}\:\mathrm{must}\:\mathrm{be} \\ $$$$\mathrm{excluded}\left(\mathrm{i}\:\mathrm{mistaked}``\:\mathrm{including}\:''\mathrm{and}\right. \\ $$$$\left.``\mathrm{excluding}\:''\mathrm{in}\:\mathrm{English}\right) \\ $$

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