doubt for word problem experts

Question

A car travels the first 1/3 of a certain distance with speed of 10km/h the next 1/3 distance with a speed of 20km/h and the last 1/3 distance with a speed of 60km/h the average speed of the car for whole journey is

 

i know the solution but i want to find out where did i mistake

now we want to find out average speed

avg speed = total distance/total time

 

now let total distance be x

 

first x*1/3 

 

all three distance is x/3+x/3+x/3

now total time = speed/distance

      total time =   x/3/10+x/3/20+x/3/60

 

equation should be 

                      x/3+x/3+x/3

avg speed =   x/3/10+x/3/20+x/3/60

 

but answer is wrong please explain me how it is wrong

 

 

 

Answer 1

Hi Amey, if we let x be the total distance, then we have the following:

 

Time at 10 km/h is equal to (x/3) / 10 or x/30 hours.

 

Time at 20 km/h is equal to (x/3) / 20 or x/60 hours.

 

Time at 30 km/h is equal to (x/3) / 30 or x/90 hours.

 

Total time is equal to x/30 + x/60 + x/90

 

The common denominator for 30, 60, and 90 is 180.

 

This gives:

 

Total time = 6x/180 + 3x/180 + 2x/180, or 11x/180

 

To get the average speed, divide the total distance, x, by the total time, 11x/180.

 

Average speed = x / (11x/180)

 

Average speed = 180x / 11x

 

Average speed = 180 / 11

 

Average speed ≈ 16.36 km/h

 

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