A man travels for 5 hours 15 minutes. If he covers the first half of the journey at 60 km/hr and rest at 45 km/hr. Find the total distance travelled by him ?

Solution(By Examveda Team)

Let ther distance covered be 2x km
$${{\text{Time}} = \frac{{{\text{Distance}}}}{{{\text{Speed}}}}}$$
Time taken to covers the first half and second half of the journey in t₁ hours and t₂ hours
$$\eqalign{ & \Rightarrow \frac{a}{{60}} = {t_1}.....(i) \cr & \Rightarrow \frac{a}{{45}} = {t_2}.....(ii) \cr} $$
Adding (i) and (ii) we get
$$\eqalign{ & \Leftrightarrow \frac{a}{{60}} + \frac{a}{{45}} = {t_1} + {t_2} \cr & \Leftrightarrow \frac{a}{{60}} + \frac{a}{{45}} = 5\frac{{15}}{{60}} \cr & \Leftrightarrow \frac{a}{{60}} + \frac{a}{{45}} = 5\frac{1}{4} \cr & \Leftrightarrow \frac{{3a + 4a}}{{180}} = \frac{{21}}{4} \cr & \Leftrightarrow 7a = \frac{{21}}{4} \times 180 \cr & \Rightarrow a = \frac{{21 \times 180}}{{4 \times 7}} \cr & \Rightarrow a = 135{\text{ km}} \cr} $$
∴ Length of total journey :
= (2 × 135) km
= 270 km