A man can walk from A to B and back in a certain time at 7 km/hr. If he walks from A to B at 8 km/hr and returns from B to A at 6 km/hr he takes 2 minutes more. Find the distance between A and B.

We calculate the speed by dividing the distance over time:

s = d/t

So the distance described in the problem is always the same, A to B and B to A.

But we are told that;

7 = d/t

7 = 2d / (t + 2)

that is, the first equation say that at speed 7 km/h a distance d is walked in a time t

the second equation say that at a average speed of 7 (that is 8 on one way and 6 in the other: 8 + 6 = 14, half of it), twice the distance is walked in a time equal to the first time plus 2 minutes.

So we have a system of linear equations, 2 of them with two unknowns, we can solve that:

7 = d/t

7 = 2d / (t + 2)

lets simplify them:

7t = d

7 (t + 2) = 2d

7t = 2d - 14

we substitute the first in the second:

7t = 2d - 14

7t = d

so:

d = 2d - 14

d = 14

so the distance between A and B is 14 km