A bus travelled a total distance s.It covered it's journey in consecutive one-fourth distances with speeds 60km/hr,50km/hr,70km/hr,80km/hr, respectively.Calculate the average speed of bus for entire journey.
Answers
Given : A bus travelled a total distance s .It covered its journey in consecutive one-fourth distances with speeds 60 km/hr ,50 km/hr ,70km/hr ,80km/hr respectively.
To find : The average speed of bus for entire journey.
solution : time taken to travel (s/4) with speed 60 km/h , t₁ = (s/4)/60 = (s/240) hrs
time taken to travel (s/4) with speed 50 km/h, t₂ = (s/4)/50 = (s/200) hrs
time taken to travel (s/4) with speed 70 km/h, t₃ = (s/4)/70 = (s/280) hrs
time taken to travel (s/4) with speed 80 km/h, t₄ = (s/4)/80 = (s/320) hrs
average speed = total distance/total time taken
= s/[t₁ + t₂ + t₃ + t₄]
= s/[(s/240) + (s/200) + (s/280) + (s/320)]
= 1/[1/240 + 1/200 + 1/280 + 1/320 ]
= 1/[(140 + 168 + 120 + 105)/33600]
= 33600/(533)
= 63.04 km/h
Therefore the average speed of bus for entire journey is 63.04 km/h.
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