A person travels from P to Q at a speed of 50 km/h for 30 minutes. He then increases his speed to 60 km/h and reaches his destination R in 20 minutes. What is his average speed for the whole journey?

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

From P to Q

Speed = 50 km/hr

$$Time= 30 min = \frac{1}{2} hr $$

$$ Distance = speed \times time $$

$$ Distance = 50 km/hr \times \frac{1}{2} hr $$

Solving, $$ Distance =25 km $$

To R

Speed = 60 km/hr

$$Time= 20 min = \frac{1}{3} hr $$

$$ Distance = speed \times time $$

$$ Distance = 60 km/hr \times \frac{1}{3} hr $$

Solving, $$ Distance =20 km $$

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

Total distance = 25+20=45

$$ Total time = \frac{1}{2} +\frac{1}{3} = \frac{5}{6} $$

On solving,

 Average speed = 54 km/hr