A person wanted to travel from charbag to aalambag with an average speed of $60$km/h by car. The distance between the two cities is $2$ km. Due to traffic he could travel at $30$ km/h for the first km. What should his speed be for the remaining journey to achieve his average speed target of $60$km/h.
a) can't achieve his target with any finite speed.
b) $60$km/h
c) $90$km/h
d) $120$km/h
The formula for average speed is $$v_{avg} = \frac{\text{total distance}}{\text{total time}}= \frac{d_1+d_2}{t_1+t_2}$$
$$d_1= 1\text{km},v_1 = 30\text{km/h} \implies t_1 = \frac{1}{30}h$$
$$d_2 = 1\text{km},v_1 = x\text{km/h} \implies t_1 = \frac{1}{x}h$$ So, $$60 = \frac{1+1}{\frac{1}{30}+\frac{1}{x}}$$
Find $x$ from here if possible (finite positive value) , otherwise he can't achieve his target with any finite speed.
