Amey B.

asked • 05/09/16

doubt for word problem experts

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
 
 
 

1 Expert Answer

By:

Amey B.

answer is 18
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05/09/16

Don L.

tutor
Hi Amey, The total time should have been x/30 + x/60 + x/180. The common denominator is still 180, but the total time becomes 10x/180 instead of 11x/180.
 
Then the average would be x / (10x/180) or 180/10, which is 18.
 
I miss read the description.
 
OK?
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05/09/16

Amey B.

how it can 10x/180
total time is 6x/180 + 3x/180 + 2x/180
that is 11x/180
if this 11x/180 is total time so our solution is worng
 
explain me how 10x/180 is total time
 
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05/11/16

Don L.

tutor
Hi Amey, the fractions are: x/30 from (x/3)/10, x/60 from (x/3)/20, and x/180 from (x/3)/60.
 
Using the common denominator of 180 gives: 6x/180 + 3x/180 + x/180 or 10x/180.
 
OK?
 
 
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05/11/16

Amey B.

yes i understood sir
but i have other doubt that is now we tried assuming x as total distance 
now can we take x as total time i have already tried but it goes wrong
if you know then please explain me
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05/12/16

Don L.

tutor
Hi Amey, keep in mind, the time will change for each 1/3 of the trip because the faster you go, the less time it will take to cover 1/3 of the total distance. Let d be the total distance. Then the total time for the trip will be:
 
Total time = (d/3)/10 + (d/3)/20 + (d/3)/60
 
Total time = d/30 + d/60 + d/180
 
Common denominator is still 180:
 
Total time = 6d/180 + 3d/180 + d/180, or 10d/180
 
Average = total distance / total time
 
Average = d/(10d/180)
 
Average = 18 km/h
 
Questions?
 
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05/12/16

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