Question

during 1st half of the journey a body travels with a speed of 40km/h and in the 2nd half it travels with speed of 20km h calculate average speed of the whole journey.

Answer 1

Let the total distance  be  2x .

in first  half journey,

$distance = x \\ \\ speed = 40 \ km/h \\ \\ time (t_1) = \frac{distance}{speed}  \\ \\ t_1 =  \frac{x}{40}$

in second  halg  journey,

$distance = x \\ \\ speed = 20 \ km/h \\ \\ time (t_2) = \frac{distance}{speed}  \\ \\ t_1 =  \frac{x}{20} \\ \\  \text{We know that, } \\ \\ \text{Average Speed} = \frac{total \ distance}{total \ time}  = \frac{2x}{t_1 + t_2} \\ \\ = \frac{2x}{ \frac{x}{40} + \frac{x}{20} }  \\ \\  = \frac{2}{ \frac{1}{40} + \frac{1}{20} } \\ \\ = \frac{40}{ \frac{1}{2} + 1 } \\ \\ = \frac{80}{3} \  km/h$

Answer 2

The average speed for the whole journey would be 30km.

For this, we do not even need to calculate the speed of the object, that has already been given. We have also been given the time of the journey as x

For 1st half the body travels at 40 km/h i.e. 1/2 x journey.

For the second half the body travels at 20 km/h i.e. 1/2x journey.

Hence, in order to calculate the avergae, we simply 40 + 20 = 60 and then divided 60/2

Which is 30km/h