Question

32. Places A and B are 100 km apart from each other on a highway. A car starts from A and another
starts from B at the same time. If they move in the same direction, they meet in 5 hours and if they
move in opposite directions, they meet in 1 hour. Find the speed of the cars.
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Answer 1

Step-by-step explanation:

speed of carA be a and car B be b

s×t =distance

1(a)+1(b)=100

a +b =100.........1

then,

5(a)-5(b)=100

5(a - b)=100

a - b=20.........2

add 1 and 2

a+b= 100

a - b = 20

= 2a = 120

a= 60 km/hr

b= 40km/hr

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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