Question

04. When two bodies move uniformly towards each
other the dist.between them decreases by 8 m/s If
both bodies move in the same direction with
diff.speeds the distance between them increases by
2 m/s.
The speeds of two bodies will be
(1) 4 m/s and 3 m/s (2) 4 m/s and 2 m/s
(3) 5 m/s and 3 m/s (4) 1 m/s and 3 m/s​

Answer 1

Answer:

5m/s 3m/s

Explanation:

x+y=8

x-y=2

add both eqn we will get

x=5 and put value of x in in any eqn you will get y=3

Answer 2

Given :

• Speed of the body when they are coming towards each other = 8 m/s

• Speed of the body when they are moving from each other = 2 m/s

To find :

Orginal speed of the body.

Solution :

Let the orginal speed of first body be x and the speed of second body be y.

Now ,

According to the question , when the body are coming towards each other the distance is decreasing by 8 m/s.

So, here the Equation will be :

$\boxed{\therefore \bf{x + y = 8}}$⠀⠀⠀⠀⠀⠀⠀Eq.(i)

A/c ,when the bodies are moving away from each other , the distance increases by 2 m/s.

So , here the Equation formed will be :

$\boxed{\therefore\bf{x - y = 2}}$⠀⠀⠀⠀⠀⠀⠀Eq.(ii)

Now to find the speed of the two bodies , we can easily solve for x and y by solving the Equation (i) and (ii).

By adding Eq.(ii) from Eq.(ii) , we get :

$:\implies \bf{(x + y) + (x - y) = 8 + 2}$

$:\implies \bf{x + y + x - y = 8 + 2}$

$:\implies \bf{x + \not{y} + x - \not{y} = 8 + 2}$

$:\implies \bf{x + x = 10}$

$:\implies \bf{2x = 10}$

$:\implies \bf{x = \dfrac{10}{2}}$

$:\implies \bf{x = 5}$

$\boxed{\therefore \bf{x = 5}}$

Now substituting the value of x in Equation (i) , we get :

$:\implies \bf{x + y = 8}$

$:\implies \bf{5 + y = 8}$

$:\implies \bf{y = 8 - 5}$

$:\implies \bf{y = 3}$

$\boxed{\therefore \bf{y = 3}}$

Since, we have taken the speed of first body as x and the speed of other body as y , we get that :

• Speed of first body = x = 5 m/s.

• Speed of second body = y = 3 m/s.

Hence, the speed of first body is 5 m/s and the speed of other body is 3 m/s.