A train travels 20 km at a uniform speed of 60 km/h and the next 20 km at a uniform speed of 80 km/hr. calculate its average speed.

                               

A train travels 20 km at a uniform speed of 60 km/h and the next 20 km at a uniform speed of 80 km/hr. calculate its average speed.

Given:

• First distance $d_1 = 20 \, \text{km}$, speed $v_1 = 60 \, \text{km/h}$
  

• Second distance $d_2 = 20 \, \text{km}$, speed $v_2 = 80 \, \text{km/h}$
  

Step 1: Time taken for each part

$$t_1 = \frac{20}{60} = \frac{1}{3} \text{ h}$$
$$t_2 = \frac{20}{80} = \frac{1}{4} \text{ h}$$

Step 2: Total distance and total time

$$\text{Total distance} = 20 + 20 = 40 \text{ km}$$
$$\text{Total time} = \frac{1}{3} + \frac{1}{4} = \frac{4 + 3}{12} = \frac{7}{12} \text{ h}$$

Step 3: Average speed

$$\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{40}{7/12} = \frac{40 \times 12}{7} = \frac{480}{7}$$ $$\text{Average speed}\approx 68.6\text{ km/h}$$