Arjun cycles 36 km to his grandmother's house.

Step 1. The equation. $\dfrac{36}{v} - \dfrac{36}{v + 3} = 1$. Multiply by $v(v + 3)$: $36(v + 3) - 36v = v(v + 3)$, so $v^2 + 3v - 108 = 0$.

Step 2. The discriminant. $9 + 432 = 441 = 21^2$.

Step 3. The formula. $v = \dfrac{-3 \pm 21}{2}$, so $v = 9$ or $v = -12$.

Step 4. Choose. A speed cannot be negative, so $v = 9$. Check: $36 \div 9 = 4$ hours, and $36 \div 12 = 3$ hours, one hour less.