Question

A body covers half the distance between two points at 40 k.m/ h and next half at 60 k.m/ h.calculate its average speed​

Answer 1

Answer: 48 km/hr

Explanation:

(Note - If you want a quick answer, then just read what is written in bold and the equations.)

Now, it's a common misconception that average speed is calculated by taking the average of the given speeds. But it's not like that.

$Average \ speed = \dfrac{Total \ distance}{Total \ time}$

You might ask, why can't we just take the average of the given speeds. The answer to this question is that speed, here, is not an independent quantity. It is dependent on two other quantities, i.e., distance and time.

SO REMEMBER:-

$Average \ speed = \dfrac{Total \ distance}{Total \ time}$

Now, let's find the total distance and the total time taken to cover that distance.

Let the total distance covered be = $x$ km

∴ Half the distance = $x/2$ km

So, the first half distance, i.e., $x/2$ km is covered by the speed of 40 km/hr.

Let's calculate the time taken to cover this distance

Distance = $x/2$ km

Speed = 40 km/hr

$Speed = \dfrac{Distance}{Time}$

$Time = \dfrac{Distance}{Speed}$

$Time = \dfrac{\frac{x}{2} }{40}$

$Time = \dfrac{x}{80}$

∴ Time taken to cover the first half distance = $x/80$ hr

Similarly, let's calculate the time taken to cover the second half distance.

Distance = $x/2$ km

Speed = 60 km/hr

$Speed = \dfrac{Distance}{Time}$

$Time = \dfrac{Distance}{Speed}$

$Time = \dfrac{\frac{x}{2} }{60}$

$Time = \dfrac{x}{120}$

∴ Time taken to cover the second half distance = $x/120$ hr

Now, let's find the total time taken to complete the journey.

$Total \ time = \dfrac{x}{80} + \dfrac{x}{120}$

$Total \ time = \dfrac{3x}{240} + \dfrac{2x}{240}$

$Total \ time = \dfrac{3x + 2x}{240}$

$Total \ time = \dfrac{5x}{240}$

$Total \ time = \dfrac{x}{48}$

∴ Total time taken = $x/48$ hr

We now know the total distance and the total time. So, just put their values in the formula to find average speed.

$Average \ speed = \dfrac{Total \ distance}{Total \ time}$

$Average \ speed = \dfrac{x}{\frac{x}{48}}$

$Average \ speed = \dfrac{48x}{x}}$

$Average \ speed = \dfrac{48}{1}}$

Therefore, average speed = 48 km/hr.