A Train has speed 60 km/hr for one -hr and 40km/hr for next half-hr, then average speed in km/hr. (a) 50 (b) 53.33 (c) 48 (d) 70

Step-by-step solution

1. 1

   Given data

   Speed $v_1 = 60 \text{ km/hr}$ for time $t_1 = 1 \text{ hr}$. Speed $v_2 = 40 \text{ km/hr}$ for time $t_2 = 0.5 \text{ hr}$.
2. 2

   Average speed formula

   Average speed is total distance divided by total time.

   $$\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}$$
3. 3

   Calculate distances

   Distance $d = v \times t$. Calculate $d_1$ and $d_2$.
4. 4

   Distance for first segment

   $d_1 = v_1 \times t_1 = 60 \text{ km/hr} \times 1 \text{ hr}$

   $$d_1 = 60 \text{ km}$$
5. 5

   Distance for second segment

   $d_2 = v_2 \times t_2 = 40 \text{ km/hr} \times 0.5 \text{ hr}$

   $$d_2 = 20 \text{ km}$$
6. 6

   Total distance and time

   Total distance $D = d_1 + d_2$. Total time $T = t_1 + t_2$.

   $$D = 60 + 20 = 80 \text{ km}, T = 1 + 0.5 = 1.5 \text{ hr}$$
7. 7

   Calculate average speed

   Average speed $= \frac{D}{T} = \frac{80 \text{ km}}{1.5 \text{ hr}}$

   $$\text{Average Speed} = 53.33 \text{ km/hr}$$