If a person goes from home to his college at a speed of 12 km/h, he reaches 7 minutes early. If he goes at a speed of 8 km/h, he reaches 14 minutes late. What is the distance between his home and his college?

Let's assume the distance between his home and his college is 'd' km.

If a person goes from home to his college at a speed of 12 km/h, he reaches 7 minutes early.

Let's assume the usual time (on time) taken to cover the distance is 't' hours.

$$\frac{distance}{speed}\ =\ time$$

$$\frac{d}{12}\ =\ t-\frac{7}{60}$$

$$\frac{d}{12}+\frac{7}{60} = t$$    Eq.(i)

If he goes at a speed of 8 km/h, he reaches 14 minutes late.

$$\frac{d}{8}\ =\ t+\frac{14}{60}$$

$$\frac{d}{8}-\frac{14}{60} = t$$    Eq.(ii)

So Eq.(i) = Eq.(ii)

$$\frac{d}{12}+\frac{7}{60} = \frac{d}{8}-\frac{14}{60}$$

$$\frac{7}{15}+\frac{14}{15}=\frac{d}{2}-\frac{d}{3}$$