Question

6. A car covers the first half of the distance between two places at a speed of 40 km/h and the
second half at 60 km/h. What is the average speed of the car?
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Answer 1

Given ,

"  A car covers the first half of the distance between two places at a speed of 40 km/h and the  second half at 60 km/h. What is the average speed of the car "

Method - 1 : ( Complex method )

Let the first half of distance be " x " km

So the second half distance is also " x " km

Distance 1 = x

Speed 1 = 40 km/h

Since , Speed = Distance / Time

⇒ Time 1 = Distance 1 / Speed 1

⇒ Time 1 = x / 40

Distance 2 = x

Speed 2 = 60 km/h

⇒ Time 2 = x / 60

Total time , T = Time 1 + Time 2

⇒ T = x/40 + x/60

⇒ T = x / 24

Total Distance , D = D1 + D2

⇒ D = x + x

⇒ D = 2x

Now " Average speed is defined as Total distance covered per total time "

⇒ Average Speed = D / T

⇒ Average speed = 2x / ( x/24 )

⇒ Average Speed = 48 km/h

Method - 2 : ( Shortcut method )

We have a formula for Average Speed when we have two speeds.

Here ,

v1 = 40 km/h , v2 = 60 km/h

$\bf v_{avg}=\dfrac{2.v_1.v_2}{v_1+v_2}\\\\\implies v_{avg}=\dfrac{2*40*60}{40+60}\\\\\implies v_{ang}=48\;km/h$

So Average speed of the car is 48 km/h