A person covers 40% of a distance with a speed of 60 km/h and the remaining with a speed of 40 km/h. What is his average speed for the whole journey in km/h?

Let the total distance covered = $$L$$ km

Time taken by the person to cover 40% distance =$$\frac{\frac{40}{100}L\ }{60}=\frac{40L}{60\times100}=\frac{2L}{3\times100}$$

Time taken by the person to cover 60% distance =$$\frac{\frac{60}{100}L\ }{40}=\frac{60L}{40\times100}=\frac{3L}{2\times100}$$

$$\therefore\ Average  Speed=\frac{Total\ Dis\tan ce}{Total\ Time}=\frac{L}{\frac{2L}{3\times100}+\frac{3L}{2\times100}}=\frac{L}{\frac{1}{100}\left[\frac{2L}{3}+\frac{3L}{2}\right]}=\frac{100L}{\frac{13L}{6}}=\frac{100L\times6}{13L}=\frac{600}{13}$$