Question

16.Points A and B are 60 km apart.On car starts from A and another from B at the same time .If they go in the same direction ,they meet in 6 hours and if they go in opposite direction they meet in 2 hours.The speed of the car with the greater speed is *​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Correct Question:

Points A and B are 60 km apart. One car starts from A and another from B at the same time .If they go in the same direction, they meet in 6 hours and if they go in opposite direction then they meet in 2 hours. Find the speed of the car with the greater speed.

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Answer:-

$\sf{The \ speed \ of \ car \ starting \ at \ point \ A \ is }$

$\sf{greater, \ it \ is \ 20 \ km \ hr^{-1}}$

Given:

• Points A and B are 60 km apart. One car st.arts from A and another from B at the same time.

• If they go in the same direction, they meet in 6 hours and if they go in opposite direction they meet in 2 hours.

• If they go in opposite direction then they meet in 2 hours.

To find:

• Find the speed of the car with the greater speed.

Solution:

$\sf{Let \ the \ speed \ of \ car \ which \ starts \ from \ point}$

$\sf{A \ be \ x \ km \ hr^{-1} \ and \ speed \ of \ car \ which}$

$\sf{starts \ from \ point \ B \ be \ y \ km \ hr^{-1}}$

$\boxed{\sf{Distance=Time\times \ Speed}}$

$\sf{According \ to \ the \ first \ condition. }$

$\sf{\underline{\underline{Concept:}}}$

$\sf{Both \ cars \ meet \ each \ other \ after \ 6 \ hours,}$

$\sf{but \ distance \ between \ them \ is \ 60 \ km.}$

$\sf{Hence, \ car \ at \ point \ A \ travels \ distance \ of}$

$\sf{60 \ km \ more \ than \ car \ at \ paint \ B.}$

$\sf{6x-6y=60}$

$\sf{\therefore{6(x-y)=60}}$

$\sf{\therefore{x-y=\frac{60}{6}}}$

$\sf{\therefore{x-y=10...(1)}}$

$\sf{According \ to \ the \ second \ condition. }$

$\sf{\underline{\underline{Concept:}}}$

$\sf{Both \ cars \ travel's \ to \ each \ other.}$

$\sf{Hence, \ distance \ travelled \ by \ them \ is \ equal \ to}$

$\sf{distance \ between \ them.}$

$\sf{2x+2y=60}$

$\sf{\therefore{2(x+y)=60}}$

$\sf{\therefore{x+y=\frac{60}{2}}}$

$\sf{\therefore{x+y=30...(2)}}$

$\sf{Add \ equations \ (1) \ and \ (2)}$

$\sf{x-y=10}$

$\sf{+}$

$\sf{x+y=30}$

_________________

$\sf{2x=40}$

$\sf{\therefore{x=\frac{40}{2}}}$

$\sf{\therefore{x=20}}$

$\sf{Substitute \ x=20 \ in \ equation(2)}$

$\sf{20+y=30}$

$\sf{\therefore{y=30-20}}$

$\sf{\therefore{y=10}}$

$\sf\purple{\tt{\therefore{The \ speed \ of \ car \ starting \ at \ point \ A \ is }}}$

$\sf\purple{\tt{greater, \ it \ is \ 20 \ km \ hr^{-1}}}$