Places a and b are 80 km apart from each other on a highway. A car starts from a and another from b at the same time. If they move in same direction they meet in 8 hrs and if they move towards each other they meet in 1 hr 20 mins. Find the speed of the car.
Answers
let the speed of the car starting from A be x km per hour that of the car starting from B be y kilometres per hour distance between two cars is 80 km
if we travel in the same Direction they meet after 8 hrs
distance travelled by cars starting from A in 8 hours =8x kilometre
the distance travelled by the car from B=8y km
8x-8y=80
x-y=10.....dividing by 8 ...(1)
if they travel towards each other the total distance travelled by them will be 80
kilometre
in 1 hour 20 minutes the distance travelled by the car starting from A is equal to x kilometres and that by the car from B equal to y km
1.20 x +1.20y =80km... (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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