Points A and B are 90 km apart from each other on a highway. A car starts from A and another from B at the same time. If they go in the same direction, they meet in 9 hours, and if they move in opposite directions, they meet in 9/7 hours .Find the speed of each car.
Answers
let the speed of car starting from a be 'x' km/h and speed of car starting from b be 'y' km/h
∴total distance=80 km
⇒ 1 hour 20 mins= 4/3 hour
given that when car moves in same direction,
∴distance travelled by y= 8y km
∴distance travelled by x= 8x= 80+8y
⇒equation formed is 8x=80+8y
=> 8x-8y=80
=> x-y=10 ..................1
agai for opposite direction,
∴distance travelled by x= (4/3)x
∴distance travelled by y= (4/3) y
⇒total distance covered= 4/3*x+4/3y
=> 80= 4x+4y/3
=> 240= 4x+4y
=> 60=x+y ...............2
from equation 1 and 2 we get
60=x+y ...........2
x-y=10 .........1
=> x= 10+y ..........3
after substituting the value of equation 3 in equation 2
60= 10+y+y
=> 60-10=2y
=> 50=2y
=> 25=y
⇒x=10+y=> x= 10+25=> x=35
∴the speed of car starting from a is 35km/h
∴the speed of car starting from b is 25km/h..
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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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