Let distance = x km

Usual speed = y km/h.

Equation for faster speed

= x ( y + 2) - xy / y( y + 2) = 1 / 6

= xy + 2x - xy / y( y + 2) = 1 / 6

= 2x / y( y + 2) = 1 / 6

= 12x = y( y + 2)........(1)

Equation for slower speed

= xy - x ( y - 4) / y( y - 4) = 2 / 3

= (xy - xy + 4x ) / y( y - 4) = 2 / 3

= 4x / y( y - 4) = 2 / 3

= 12x = y( y - 4)........(2)

Now divide the equation (1) with (2)

12/12 = ( y + 2) / ( y - 4)

1/1 = ( y + 2) / ( y - 4)

1y - 4 = 1y + 2

1y - 1y = 2 + 4

0y = 6

y = 1 / 0

putting the value of y in equation (1)

12x = 1 / 0( 1 / 0 + 2)

x = 0.25 km

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