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  • Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method : (iv) 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

Q4. Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:

(iv) 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?

Answers (1)

best_answer

Let the speed of the first car be x and the speed of the second car be y.

Let's solve this problem by using relative motion concept,

the relative speed when they are going in the same direction = x - y 

the relative speed when they are going in the opposite direction = x + y

The given relative distance between them = 100 km.

Now, as we know,

Relative distance = Relative speed * time .

So, according to the question,

5\times(x-y)=100

 \Rightarrow 5x-5y=100

\Rightarrow x-y=20.........(1)

Also,

1(x+y)=100

\Rightarrow x+y=100........(2)

Now, by adding (1) and (2), we get

2x=120

\Rightarrow x=60

putting this in (1)

60-y=20

\Rightarrow y=60-20

\Rightarrow y=40

Hence, the speeds of the cars are 40 km/hour and 60 km/hour.

Posted by

Pankaj Sanodiya

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