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Question Number 26623 by bbbbbb last updated on 27/Dec/17

distance between 2 places A and B on road is 70 km. a car starts from A and other from B .if they travel in same direction they will meet after 7 hours. if they travel towards each other they will meet after 1 hour then find their speeds

$$\mathrm{distance}\:\mathrm{between}\:\mathrm{2}\:\mathrm{places}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{on} \\ $$$$\mathrm{road}\:\mathrm{is}\:\mathrm{70}\:\mathrm{km}.\:\mathrm{a}\:\mathrm{car}\:\mathrm{starts}\:\mathrm{from}\:\mathrm{A}\:\mathrm{and}\:\mathrm{other}\: \\ $$$$\mathrm{from}\:\mathrm{B}\:.\mathrm{if}\:\mathrm{they}\:\mathrm{travel}\:\mathrm{in}\:\mathrm{same}\:\mathrm{direction} \\ $$$$\mathrm{they}\:\mathrm{will}\:\mathrm{meet}\:\mathrm{after}\:\mathrm{7}\:\mathrm{hours}.\:\mathrm{if}\:\mathrm{they}\:\mathrm{travel} \\ $$$$\mathrm{towards}\:\mathrm{each}\:\mathrm{other}\:\mathrm{they}\:\mathrm{will}\:\mathrm{meet}\:\mathrm{after} \\ $$$$\mathrm{1}\:\mathrm{hour}\:\mathrm{then}\:\mathrm{find}\:\mathrm{their}\:\mathrm{speeds} \\ $$

Answered by mrW1 last updated on 28/Dec/17

v_A −v_B =((70)/7)=10 km/h v_A +v_B =((70)/1)=70 km/h ⇒v_A =((70+10)/2)=40 km/h ⇒v_B =((70−10)/2)=30 km/h

$${v}_{{A}} −{v}_{{B}} =\frac{\mathrm{70}}{\mathrm{7}}=\mathrm{10}\:{km}/{h} \\ $$$${v}_{{A}} +{v}_{{B}} =\frac{\mathrm{70}}{\mathrm{1}}=\mathrm{70}\:{km}/{h} \\ $$$$\Rightarrow{v}_{{A}} =\frac{\mathrm{70}+\mathrm{10}}{\mathrm{2}}=\mathrm{40}\:{km}/{h} \\ $$$$\Rightarrow{v}_{{B}} =\frac{\mathrm{70}−\mathrm{10}}{\mathrm{2}}=\mathrm{30}\:{km}/{h} \\ $$

Answered by Rasheed.Sindhi last updated on 28/Dec/17

Case-1: If the cars travel in same direction. Let the cars meet at C such that BC=x kms ⇒ AC=x+70 kms CarA: x+70 kms in 7 hours ∴ Speed: ((x+70)/7) km/h CarB: x kms in 7 hours ∴ Speed: (x/7) km/h Case-2: If the cars travel in opposite direction. Let the cars meet at D such that AD=y kms ⇒ BD=70−y kms CarA: y kms in l hour. ∴Speed: y km/h CarB: 70−y kms in l hour. ∴ Speed: 70−y km/h As the cars have same speed in both cases: ((x+70)/7)=y ∧ (x/7) =70−y (x/7) =70−((x+70)/7) x=490−x−70 x=210 kms y= ((x+70)/7)= ((210+70)/7)=40 kms Speed of CarA=y km/h=40 km/h Speed of CarB=70−y km/h=30 km/h

$$\mathrm{Case}-\mathrm{1}:\:\mathrm{If}\:\mathrm{the}\:\mathrm{cars}\:\mathrm{travel}\:\mathrm{in}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{same}\:\mathrm{direction}. \\ $$$$\:\mathrm{Let}\:\mathrm{the}\:\mathrm{cars}\:\mathrm{meet}\:\mathrm{at}\:\mathrm{C}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{BC}=\mathrm{x}\:\mathrm{kms}\:\Rightarrow\:\mathrm{AC}=\mathrm{x}+\mathrm{70}\:\mathrm{kms} \\ $$$$\:\mathrm{CarA}:\:\:\mathrm{x}+\mathrm{70}\:\mathrm{kms}\:\mathrm{in}\:\mathrm{7}\:\mathrm{hours} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\therefore\:\mathrm{Speed}:\:\frac{\mathrm{x}+\mathrm{70}}{\mathrm{7}}\:\mathrm{km}/\mathrm{h} \\ $$$$\mathrm{CarB}:\:\mathrm{x}\:\mathrm{kms}\:\mathrm{in}\:\mathrm{7}\:\mathrm{hours} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\therefore\:\mathrm{Speed}:\:\frac{\mathrm{x}}{\mathrm{7}}\:\mathrm{km}/\mathrm{h} \\ $$$$\mathrm{Case}-\mathrm{2}:\:\mathrm{If}\:\mathrm{the}\:\mathrm{cars}\:\mathrm{travel}\:\mathrm{in} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{opposite}\:\mathrm{direction}. \\ $$$$\:\mathrm{Let}\:\mathrm{the}\:\mathrm{cars}\:\mathrm{meet}\:\mathrm{at}\:\mathrm{D}\:\mathrm{such}\:\mathrm{that}\:\:\:\:\:\: \\ $$$$\mathrm{AD}=\mathrm{y}\:\mathrm{kms}\:\Rightarrow\:\mathrm{BD}=\mathrm{70}−\mathrm{y}\:\mathrm{kms} \\ $$$$\:\mathrm{CarA}:\:\:\mathrm{y}\:\mathrm{kms}\:\mathrm{in}\:\mathrm{l}\:\mathrm{hour}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\therefore\mathrm{Speed}:\:\mathrm{y}\:\mathrm{km}/\mathrm{h} \\ $$$$\:\mathrm{CarB}:\:\:\mathrm{70}−\mathrm{y}\:\mathrm{kms}\:\mathrm{in}\:\mathrm{l}\:\mathrm{hour}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\therefore\:\mathrm{Speed}:\:\mathrm{70}−\mathrm{y}\:\mathrm{km}/\mathrm{h} \\ $$$$\mathrm{As}\:\mathrm{the}\:\mathrm{cars}\:\mathrm{have}\:\mathrm{same}\:\mathrm{speed}\:\mathrm{in} \\ $$$$\mathrm{both}\:\mathrm{cases}: \\ $$$$\:\:\:\:\:\:\frac{\mathrm{x}+\mathrm{70}}{\mathrm{7}}=\mathrm{y}\:\:\wedge\:\:\frac{\mathrm{x}}{\mathrm{7}}\:=\mathrm{70}−\mathrm{y} \\ $$$$\:\:\:\:\:\frac{\mathrm{x}}{\mathrm{7}}\:=\mathrm{70}−\frac{\mathrm{x}+\mathrm{70}}{\mathrm{7}} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{x}=\mathrm{490}−\mathrm{x}−\mathrm{70} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{x}=\mathrm{210}\:\mathrm{kms} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{y}=\:\frac{\mathrm{x}+\mathrm{70}}{\mathrm{7}}=\:\frac{\mathrm{210}+\mathrm{70}}{\mathrm{7}}=\mathrm{40}\:\mathrm{kms} \\ $$$$\mathrm{Speed}\:\mathrm{of}\:\mathrm{CarA}=\mathrm{y}\:\mathrm{km}/\mathrm{h}=\mathrm{40}\:\mathrm{km}/\mathrm{h} \\ $$$$\mathrm{Speed}\:\mathrm{of}\:\mathrm{CarB}=\mathrm{70}−\mathrm{y}\:\mathrm{km}/\mathrm{h}=\mathrm{30}\:\mathrm{km}/\mathrm{h} \\ $$

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