A man travelled 2/5 of his journey by train, 1/3 by taxi and 1/6 by bus and the remaining 10 kilometer by foot. Find the length of the total journey.

Question

Well, it is not possible for me to travel 10 km by foot hence, that man is super human.

Answer 1

Yes, 10K is 6.2 miles; a considerable distance.

 

Let x = total journey distance

 

  by train  +   by taxi    +   by bus   +   by foot     =   total journey

    (2/5)x  +   (1/3)x    +    (1/6)x   +   10K         =   x

 

To get rid of all fractions, multiply by the LCM of the denominators (this is just like finding the Least Common Denominator).    LCM = 30

 

      12x     +   10x      +      5x       +    300K        =   30x

        27x + 300K =  30x       [group like terms]

         300K =  3x                [subtract 27x from both sides]

          100K = x                 [divide both sides by 3]

 

The total journey was 100 K    (how many miles is that?)

Answer 2

Hi Rachelle,

 

The first thing you have to realize is that the 10 Km is

 

1-2/5-1/3-1/6 of his journey

 

The LCM is 30, so we have

 

30       12      10       5       30-12-10-5         3           1

---  -   ---- -  ---- -  --- =  ---------------  = ----   =  ----- = .10

30       30      30     30             30               30          10

 

 

If the 10 Km is 1/10 of the trip, then the total trip is  10/(.1) = 100 Km

Answer 3

Rachelle, believe it or not, a lot of people run 10k regularly!

 

Remember that the whole is the sum of its parts.

 

2/5 + 1/3 + 1/6 = 12/30 + 10/30 + 5/30 = 27/30 = 9/10

 

This means that the 10 km is the last 1/10 of the journey. If all 10 parts then are 10 km, 10(10) = 100 total km.