Question

A motorcyclist driving from a to b with a uniform speed of 30 km per hour and returns back with the speed of 20 km per hour find the average speed

Answer 1

To find the average speed in such case where distance travelled by the object is same, we use the formula: 2v1*v2/v1+v2
where v1 is the speed in at first journey and v2 is speed of 2nd journey.
So, = 2x30x20/30+20
=1200/50
=24 km/hr.

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Answer 2

average speed = Total distance / total time

let time taken to go from A to B = t
then,
$distance = 30t \\ time \: taken \: to \: return \: = \frac{30t}{20} = \frac{3t}{2}$
Total distance =30t + (20×3t/2)
= 30t + 30t
= 60t

total time taken= t+3t/2
= 5t/2

$average \: speed = \frac{60t}{ \frac{5t}{2} } \\ = 60t \times \frac{2}{5t} \\ = 24 \: kmph$
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