Question

Points A and B are 150 km apart on a highway. A car starts from A and another car starts from B simultaneously. If they travel in the same direction, they meet in 15 hours, but if they travel towards each other, they meet in 5 hours. Find the speed of the two cars.

( Ans : 20 km / h , 10 km / h )

Class 10

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Answer 1

Hey!!


Refer to the attachment


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Answer 2

$\large{\mathfrak{HELLO \: FRIENDS!!}}$


$\large \bf{ \mathfrak{Here \: is \: your \: answer↓}}$


▶Let the speed of the cars from A and B be x km/hr and y km/hr respectively.



▶
$\huge \boxed{CASE \: 1.}$

⏩ When the two cars move in the same direction:

In this case, let them at M after 15 hours.
[ See attachment 1. ]


Then, AM = 15x km.

And, BM = 15y km.


=> AM - BM = AB.

=> 15x - 15y = 150.

=> 15( x - y ) = 150.

$\huge \bf{=> x - y = 10...........(1).}$


▶
$\huge \boxed{CASE \: 2.}$

⏩When the two cars move in the opposite direction:


↪➡ Let one car move from A to B and let the other move from B to A. Let them meet at N after 5 hours.
[ See attachment 2.]

Then, AN = 5x km and BN = 5y km.

=> AN + BN = AB.

=> 5x + 5y = 150.

=> 5 ( x + y ) = 150.


$\huge \bf{=> x + y = 30..........(2).}$


$\underline{Adding \: equation \: (1) \: and \: (2).}$

x - y = 10.
x + y = 30.
(+)..(+)...(+).
________
2x = 40.

$\huge \boxed{=> x = 20.}$

$\underline{Putting \: x \: in \: equation \: ( 1).}$

=> 20 - y = 10.

=> -y = 10 - 20.

=> - y = -10.

$\huge \boxed{=> y = 10.}$


✅✅Hence, speed of car A = 20 km/hr.✔✔

✅✅Hence, speed of car B = 10 km/hr.✔✔



$\huge \large \boxed{ \mathfrak{THANKS}}$



$\huge \large \bf \underline{ \mathfrak{Hope \: it \: is \: helpful \: for \: you}}$