Question

Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?​

Answer 1

$Let the speed of car at A be x kmph</p><p></p><p>and the speed of car at B be y kmph</p><p></p><p></p><p>when the car travel in same direction Relative Speed is x−y</p><p></p><p>Dist=100km</p><p></p><p>t=5 hours</p><p></p><p>∴  Dist =S×T</p><p></p><p>100=(x−y)5</p><p></p><p>x−y=20⟶(I)</p><p></p><p></p><p>when car travel in opp direction Relative Speed is x+y</p><p></p><p>Dist=100km</p><p></p><p>t=1 hours</p><p></p><p>Dist=ST</p><p></p><p>100=(x+y)1</p><p></p><p>x+y=100⟶(II)</p><p></p><p></p><p>Solving (I) & (II)</p><p></p><p>x−y=20</p><p></p><p>x+y=100</p><p></p><p>   2x=120</p><p></p><p>x=60km/h</p><p></p><p>y=40km/h</p><p></p><p></p><p>Speed of the car at A =60 km/h</p><p></p><p>Speed of the car at B=40 km/h</p><p></p><p>The difference of speeds is 60−40=20</p><p></p><p>$

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Answer 2

$\huge{\underline{\boxed{\sf{\purple{Answer}}}}}$

Step-by-step explanation:

Let the speed of the car at point A be x km/hr.

And let the speed of car at point B be y km/hr.️

According to the question.

cars travelling in same direction take 5 hours.

5x - 5y = 100

( 5 is common here)

therefore,

x - y = 20 ---(i)

and car travelling at different direction take 1 hour.

x + y = 100 ---(ii)

Using elimination method here,

subtracting eq i from eq ii

we get:

x + y = 100

x - y = 20

- + -

------------------

2y = 80

therefore we got, y = 40.

$\huge{\underline{\boxed{\sf{\green{y = 40.}}}}}$

From equation (ii) we get:

x + y = 100

[we get y = 40 through elimination method)

x + 40 = 100

x = 100 - 40

x = 60.

$\huge{\underline{\boxed{\sf{\pink{x = 60}}}}}$

Therefore, speed of car at a point is 60 km per hour and speed of car at B point is 40 km per hour.

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