Question

A train covers half of its journey with a speed of 30 m/s and other half with speed of 40 m/s. Calculate it's average speed for the entire journey?

Answer 1

s = total distance. t1 and t2 are durations for covering half total distance.

s/2 = 30 * t1
s/2 = 40 * t2
So total time duration = t1+t2 = s*[1/60 + 1/80]
Avg velocity = s/(t1+t2)=
240/7 m/s= 34.28 m/s

Answer 2

speed = distance/time

Take time for speed 1 as t1 and speed 2 as t2

So, average speed = d/(t1+t2)

speed 1,

30 = d/2t1  

t1 = d/2*30  ---------------1

speed 2,

40 = d/2t2

t2 = d/2*40  --------------2

Add 1 and 2 to find average speed,

t1+t2 = d/60 +d/80

t1+t2 = d[1/60 +1/80]

t1+t2 = d *[7/240]

average speed, d/(t1+t2) =240/7 = 34.28 m/s