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Question Number 27399 by Rasheed.Sindhi last updated on 06/Jan/18

A and B are walking along a  circular track.They start from  same point at 8:00 am.  A can walk 2 rounds per hour  and B can walk 3 rounds per hour.  How many times they cross each  other before 9:30 am if they walk  (i) Opposite to each other.  (ii) In same direction.                      ?

$$\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{are}\:\mathrm{walking}\:\mathrm{along}\:\mathrm{a} \\ $$$$\mathrm{circular}\:\mathrm{track}.\mathrm{They}\:\mathrm{start}\:\mathrm{from} \\ $$$$\mathrm{same}\:\mathrm{point}\:\mathrm{at}\:\mathrm{8}:\mathrm{00}\:\mathrm{am}. \\ $$$$\mathrm{A}\:\mathrm{can}\:\mathrm{walk}\:\mathrm{2}\:\mathrm{rounds}\:\mathrm{per}\:\mathrm{hour} \\ $$$$\mathrm{and}\:\mathrm{B}\:\mathrm{can}\:\mathrm{walk}\:\mathrm{3}\:\mathrm{rounds}\:\mathrm{per}\:\mathrm{hour}. \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{times}\:\mathrm{they}\:\mathrm{cross}\:\mathrm{each} \\ $$$$\mathrm{other}\:\mathrm{before}\:\mathrm{9}:\mathrm{30}\:\mathrm{am}\:\mathrm{if}\:\mathrm{they}\:\mathrm{walk} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{Opposite}\:\mathrm{to}\:\mathrm{each}\:\mathrm{other}. \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{In}\:\mathrm{same}\:\mathrm{direction}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:? \\ $$

Answered by mrW1 last updated on 06/Jan/18

v_A =2 rounds/h  v_B =3 rounds/h  (i)  2+3=5 rounds/h  ⇒1/5 h (12 minutes) per round  i.e. they cross each other every 12 minutes  from 8:00 til 9:30 that is 90 minutes    90/12=7.x  ⇒they across each other 7 times.    (ii)  3−2=1 rounds/h  ⇒1 h (60 minutes) per round  90/60=1.x  ⇒they across each other one time.

$${v}_{{A}} =\mathrm{2}\:{rounds}/{h} \\ $$$${v}_{{B}} =\mathrm{3}\:{rounds}/{h} \\ $$$$\left({i}\right) \\ $$$$\mathrm{2}+\mathrm{3}=\mathrm{5}\:{rounds}/{h} \\ $$$$\Rightarrow\mathrm{1}/\mathrm{5}\:{h}\:\left(\mathrm{12}\:{minutes}\right)\:{per}\:{round} \\ $$$${i}.{e}.\:{they}\:{cross}\:{each}\:{other}\:{every}\:\mathrm{12}\:{minutes} \\ $$$${from}\:\mathrm{8}:\mathrm{00}\:{til}\:\mathrm{9}:\mathrm{30}\:{that}\:{is}\:\mathrm{90}\:{minutes} \\ $$$$ \\ $$$$\mathrm{90}/\mathrm{12}=\mathrm{7}.{x} \\ $$$$\Rightarrow{they}\:{across}\:{each}\:{other}\:\mathrm{7}\:{times}. \\ $$$$ \\ $$$$\left({ii}\right) \\ $$$$\mathrm{3}−\mathrm{2}=\mathrm{1}\:{rounds}/{h} \\ $$$$\Rightarrow\mathrm{1}\:{h}\:\left(\mathrm{60}\:{minutes}\right)\:{per}\:{round} \\ $$$$\mathrm{90}/\mathrm{60}=\mathrm{1}.{x} \\ $$$$\Rightarrow{they}\:{across}\:{each}\:{other}\:{one}\:{time}. \\ $$

Commented by Rasheed.Sindhi last updated on 06/Jan/18

Wonderful Sir!

$$\mathrm{Wonderful}\:\mathrm{Sir}! \\ $$

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