Question

Two places a and b are 120 km apart from each other on highway. a car starts from a and another from b at the same time.if they move in same direction,they meet in 6 hours,and if they move in opposite direction,they meet in 1 hour 12 min. .find the speed of each car

Answer 1

Answer:

Step-by-step explanation:

Let,

speed of car at "a" be x kmph 

speed of car at "b" be y kmph

dis covered by car at "a" in 6 hours = 6x

dis covered by car at "b" in 6 hours = 6y

Since they are travelling in same direction, sign shouble be negative

6x - 6y = 120

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

1hr 12 min = 1 12/60 = 72/60 = 6/5 hr

Since they are travelling in opposite directions, sign should be positive.

(6/5)x + (6/5)y = 120

6x + 6y = 120×5

6x + 6y = 20×5

x + y = 100 ------------ (2)

Adding (1) and (2)

we get 2x = 120 

x = 60

Putting x = 60 in (2) 

we get y = 40 

Therefore,speeds cars are 60 km/h & 40 km/h.

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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