GATE Chemical 2018 | GA | Question: 6

Question

An automobile travels from city $A$ to city $B$ and returns to city $A$ by the same route. The speed of the vehicle during the onward and return journeys were constant at $60$ km/h and $90$ km/h, respectively. What is the average speed in km/h for the entire journey?

• A. $72$ km/h
• B. $73$ km/h
• C. $74$ km/h
• D. $75$ km/h

Comments

75km/hr

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@ Lakshman Patel RJIT

Can u plz chk the answer key?

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@srestha

right answer is 72km/hr

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lets assume distance from A-B is lcm(60,90)=180km

average speed=total distance/total time

total distance=180+180=360km  

total time=180/60+180/90=3+2=5 hour

average speed=360/5=72km/hour

so option A

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average speed when distance is constant is =2xy/x+y

Answer 1

$\text{Average Speed} = \dfrac{\text{Total Distance travelled}}{\text{Total time taken}}$

Total Distance travelled $=2d$

Total time taken $=$ Time taken from $A$ to $B$ + Time taken from $B$ to $A$

$=\dfrac{d}{60}+\dfrac{d}{90}$

Average speed $=\dfrac{2d}{\dfrac{d}{60}+\dfrac{d}{90}}=\dfrac{2d*180}{5d}=72km/hr$

Hence, option (A) is correct

Answer 2

$average speed $$=$$ total \ distance / total\ time$

                       $ = (d + d) / (d/60 + d/90)$

                        $= (2 * 60 *90) / (60 +90)$

                     $   =72 km/hr$

Comments

how total distance 60*90??

that is speed ,na?