A train has a speed of 60 km/h for the first one hour and 40 km/h for the next half hour. Its average speed in km/h is

To find the average speed of the train, we use the basic formula:

$\text{Average Speed}=\frac{\text{Total Distance Traveled}}{\text{Total Time Taken}}$

Let's break down the journey into two parts to find the total distance and total time:

Part 1: First interval of the journey
Speed ($v_1$) = 60 km/h
Time ($t_1$) = 1 hour
Distance traveled in the first part ($d_1$) is:
$d_1=v_1\times t_1=60\text{km/h}\times 1\text{h}=60\text{km}$

Part 2: Second interval of the journey
Speed ($v_2$) = 40 km/h
Time ($t_2$) = 0.5 hours (half hour)
Distance traveled in the second part ($d_2$) is:
$d_2=v_2\times t_2=40\text{km/h}\times 0.5\text{h}=20\text{km}$

Total Distance and Total Time:
Total Distance ($d$) = $d_1+d_2=60\text{km}+20\text{km}=80\text{km}$
Total Time ($t$) = $t_1+t_2=1\text{h}+0.5\text{h}=1.5\text{hours}$

Calculating the Average Speed:
$\text{Average Speed}=\frac{80\text{km}}{1.5\text{h}}\approx 53.33\text{km/h}$

Thus, the average speed of the train is 53.33 km/h.