Question

If two bodies cover the distance in ratio 2:3 in the interval time ratio 3 :2 what is the ratio of their average speeds?

Answer 1

Given :-

The distance covered by two bodies in ratio 2:3

And the time taken by both bodies in ratio. 3:2

To find :-

We have to find the ratio of their average speed !

According to formula

$\boxed{\sf{\dag\ \ Average\ speed= \dfrac{Total\ distance }{Total \ time }}}$

• Let the distance be x

• and time be y

• Then,

$\sf\bullet Distance_1(D_1)= 2x \ \ \ \ \ ; \ Time _1(T_1)= 3y\\ \\ \sf\bullet Distance_2(D_2)= 3x \ \ \ \ \ ;\ Time _2(T_2)= 2y$

• Now find the ratios of their average speed

$:\implies\sf Average\ speed = \dfrac{D_1+D_2}{T_1+T_2}\\ \\ :\implies\sf Average\ speed = \dfrac{2x+3x}{3y+2y}\\ \\ :\implies\sf Average\ speed =\dfrac{5x}{5y}\\ \\ :\implies\sf Average \ speed = \dfrac{x}{y} \\ \\ :\implies\sf Average \ speed = x:y\ \ (1:1)$

$\underline{\boxed{\sf{\dag Ratio \ of \ their\ Av.\ speed = 1:1 }}}$

Answer 2

Ratio of their average speeds is 1 : 1

Solution

We have ratio of distance covered by two body 2 : 3 , ratio of time interval 3 : 2.

We have to find ratio of their average speeds.

Let the distance covered by two body be 2d & 3d respectively.

And, time taken by two body be 3t & 2t respectively.

We know that,

★ Average speed = Total distance/Total time

◗ Finding average speed of two bodies :

Putting all values we get :

⇒ Average speed = (2d + 3d)/(3t + 2t)

⇒ Average speed = 5d/5t

⇒ Average speed = d/t

⇒ Average speed = 1/1

⇒ Average speed = 1 : 1

∴ Ratio of their average speeds is 1 : 1