If Nikhil travelled 4 km/h faster he would take 1 hour less for a journey; if he travelled 4 km/h slower he would take 1 hour 30 minutes more. How long is the journey?

Explanation

1. 01

   Faster: $\frac{d}{v} - \frac{d}{v+4} = 1$ gives $4d = v(v+4)$.

2. 02

   Slower: $\frac{d}{v-4} - \frac{d}{v} = \frac{3}{2}$ gives $4d = \frac{3}{2}v(v-4)$.

3. 03

   So $v + 4 = \frac{3}{2}(v - 4)$, giving $v = 20$ km/h.

4. 04

   $d = \frac{20 \times 24}{4} = 120$ km. Check: 6 h at 20, 5 h at 24, 7.5 h at 16.