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

$\huge \bf \red{ \mid{ \overline{ \underline{ANSWER}}} \mid}$
Speeds of cars at places A and B are 60 km/h and 40 km/ h respectively


$\bf{QUESTION}$

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?



$\bf{step \: by \: step \: explanation}$



Let the cars from A and B start at speeds x km/h and y km/h respectively

Then,

5x - 5y = 100

==> x - y = 20 ..........( 1 )

and x + y = 100..........( 2 )


Adding ( 1 ) & ( 2 ) , we get


2x = 120


=> x = 60


•°• from ( 1 ), y = 60 - 20

•°• y = 40


•°• Speeds of cars at places A and B are 60 km/h and 40 km/ h respectively



$\huge \pink{ \mid{ \boxed { \boxed{ \ulcorner{ \mathbb{THANKS}}} \mid}}}$

Answer 2

Let the speed of the first car which starts from A = x km /hr

Speed of the second car which starts from B = y km / hr

Time = distance / speed

Distance between two places A andB are 80km d = 80 km

i ) if the cars move in same direction

Relative speed of them = ( x + y )km/hr

Time = 8hr

d = 80km

8 = 80 / ( x + y )

x + y = 80 / 8

x + y = 10 ------( 1 )

ii ) if two cars moving opposite direction, Relative speed = ( x - y ) km / hr

Time = 1 hr 20 minutes

= ( 1 + 20 / 60 ) hr

= ( 80/60)

= 4/3 hr

d = 80km

4/3 = 80 / ( x -y )

x -y = ( 80 × 3 ) / 4

x - y = 60-----( 2 )

Add ( 1 ) and ( 2 ) , we get

2x = 70

x = 35

Put x = 35 in ( 1 ) we get ,

y = 25

so,

Speed of the first car = x = 35km/hr

Speed of the second car = 25km /hr

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