A cyclist goes from a place P to Q; first at 4 km/h and later at 5 km/h in 1 hour 24 minutes altogether. If the distances covered in the first and second part of the journey are in the ratio 2 : 1, when did the cyclist change his speed after start?

The cyclist travels from P to Q with two different speeds: 4 km/h and 5 km/h.

The total time = 1 hour 24 minutes = 1.4 hours.

The distances covered at each speed are in the ratio 2:1.

Time = $$\frac{\text{Distance}}{\text{Speed}}$$​​

Let the distance covered at 4 km/h be 2x, and at 5 km/h be x.

So, According to question;

​$$\frac{x}{2} + \frac{x}{5} = \frac{7}{5}\\ \ \\\frac{5x + 2x}{10} = \frac{7}{5} \\ \ \\\frac{7x}{10} = \frac{7}{5} \\ \ \\\implies x = 2$$​​

Distance covered by 4 km/h = $$2 \times x = 2\times 2 = 4 \,km$$​​

Time taken to cover = $$\frac{4}{4}$$​ = 1 hour

Thus, the cyclist changed his speed after 1 hour.