Question

ankit covered 1/2 of the distance by metro train , 1/3 of the distance by bus and rest of 6km by car for moving from Dwarka to South Extension . Find the total distance covered

Answer 1

Let total distance be x

We are given, x/2 + x/3 + 6 = x
                  So,   3x+2x+36/6 = x
                         so, 5x+36 = 6x
                             so, x = 36 

Hence, Total Distance Covered = 36 km

Answer 2

Concept: The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers and x is a variable. This equation has only one solution.

Given: Distance covered by metro train = $\frac{1}{2}$ of the distance

           Distance covered by bus = $\frac{1}{3}$ of the distance

           Distance covered by car = 6 km

To find: the total distance

Solution: Let the total distance = x km

Distance covered by metro train = $\frac{1}{2} * x$ = $\frac{x}{2}$ km

Distance covered by bus = $\frac{1}{3} * x = \frac{x}{3}$ km

Distance covered by car = 6 km

Therefore,

$\frac{x}{2} + \frac{x}{3} + 6 = x$

Now if we take the LCM of 2,3 we get 6 to make the equation equivalent

$\frac{3x + 2x + 36}{6} = x\\\\{5x + 36} = 6x\\\\6x - 5x = 36\\\\x = 36$

Therefore, the total distance covered = 36 km.

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