81. A man covers half of his journey at
6 kmph and the remaining half at 3
kmph His average speed is
a) 9 km/h
b) 4.5 km/h
c) 4 km/h
d) 3 km/h
Answers
Step-by-step explanation:
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Averagespeed
Averagespeed=
Averagespeed= 2 x y
Averagespeed= 2 x yx + y
Averagespeed= 2 x yx + y= 2×6×3
Averagespeed= 2 x yx + y= 2×6×36+3
Averagespeed= 2 x yx + y= 2×6×36+3=
Averagespeed= 2 x yx + y= 2×6×36+3= 36
Averagespeed= 2 x yx + y= 2×6×36+3= 369
Averagespeed= 2 x yx + y= 2×6×36+3= 369=4kmph
Averagespeed=2xyx+y=2×6×36+3=369=4kmph
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Answer:
Average speed as harmonic mean method
ya, average speed for two given speeds x and y is the harmonic mean of the given speeds
i.e. if average speed is u
x,u,y will be in harmonic progression. it means
1/x,1/u,1/y will be in AP (arithmetic progression)
1/u = 1/2*(1/x+1/y)
= (x+y)/2xy
hence,
u = 2xy/(x+y)
taking, x= 6 kmph and y = 3 kmph
average speed u = 2*6*3(6+3)
= 36/9
= 4 kmph
Simple Method
let the distance be 2x
half the distance i.e. x km is covered at 6 kmoh
time taken = x/6 hours
similarly time taken to cover remaining x km at 3 kmph = x/3 hours
total time taken = x/6 + x/3
= 9x/18
= x/2 hours
average speed = total distance / total time
= 2x/(x/2). ( total distance is 2x)
= 4 kmph.