Time and distance

The answer is 6 km, not 6 kmph.

Let $y$ be the distance, and $x$ be the time he needs to go there. We have an equation $\frac{5}{60}=\frac{y}{x+7}$ (because he will be late by 7 minutes) and $\frac{6}{60}=\frac{y}{x-5}$ (he went there 5 minutes before the train comes. Cross multiply, and we get two equations: $x+7=12y$ $x-5=10y$ Solve for x and y, and we get $x=65'$ , $y=6 km$ . y is the answer we need.

distance = speed * time in the first instance distance is 5 x (t+7)=5t+35 in the 2nd instance distance is 6 x (t-5)=6t-30 As both distances are equal the 2 equations are equal so t = 65mins. 65+7=72mins which is 6/5 hours. 5*(6/5)=6 {65-5=60 which is 1 hour, 1x6=6} So distance is 6km