A car travels the first 1/3 of a certain distance with speed of 10km/h

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

This is a D-I-R-T (Distance-Is-Rate-times-Time) problem.  The problem asks for overall rate, so you need (total distance)/(total time).

 

You let x=total distance.    OK so far.   D=RT and you want to find R (that is, the overall average speed)

      R = D/T

      R = x/T         [total distance is x]

   Now, for each segment, T = D/R for that portion.

      R = x / ( (x/3)/10 + (x/3)/20 + (x/3)/60) )     [insert the distances and rates]

      R = 60x / ( 6(x/3) + 3(x/3) + (x/3) )      [multiply by 1 = 60/60 to get rid of fractions]

      R = 60x / (10x/3)                           [collect terms]

      R = 60 * 3/10        [cancel 'x'; to divide by fraction, invert and multiply]

      R = 18 km/hr  

Answer 2

Hi Amey,

 

For some reason problems like this one work much better if you use a number instead of x.

 

For example, if we say that the whole distance is 60 miles, then 1/3 would be 20 miles. And for 20 miles traveling 10mhp is 2 hours. So, the next 20 miles we do 20mph. it is an hour. And the next 20 miles we do 60 mph, so, 20 min.

 

We  have 60 miles and we drive 2+1+1/3 hour, so 60/(3 1/3)=18

 

With your solution, it is hard for me to see what you relly do, because there is no parenthesis. It seems to me that you were OK at the  total time, except for this phrase "now total time = speed/distance". 

 

Please let me know if you need more assistance with this problem.

Answer 3

Take the easy road here, and utilize actual distances to help.

 

Lets make the 'certain distance' 180 km (60 km each leg)

 

leg one at 10 km/h takes 6 hours

leg two at 20 km/hr takes 3 hrs

leg three at 60 km/h takes 1 hr.

 

it took you 10 hours to travel 180 km, or 18km/h.