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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 hours and if they move towards each other they meet in 1 hour 20 minutes. Find the speed of cars.
➡️ CLASS - X
➡️ CH - 3
➡️ Linear Equations in two variables
Answers
◆ We consider the two cars starts from A and B.
◆ We have taken the speed of Car A= x km/h
and speed of Car B= y km/h.
◆ In first case,
let C be the position where the cars meet when they are travelling in same direction .
◆ In second case ,
let D be the position where the cars meet when they are travelling in opposite direction .
◆ we use d = s × t.
◆ So, In first case as the point where the two cars meet is at C
So, we subtracted distance travelled by Car B from Car A.
◆ And, in second case as the cars are coming and meeting at D , so we add the distance travelled by Car A and Car B.
◆ Ultimately, we got two equations
x - y = 10 and x + y = 60.
◆ Now, by adding both the equation we get the the value of x and y.
◆ Therefore we got the
Speed of Car A =35km/h
and Speed of Car B = 25km/h.
Answer:
Distance between A and B is 80 km .
A car starts from A and the other starts from B .
If they move in same direction , they meet in 8 hrs .
If they move towards each other they meet in 1 hr , 20 min
= 1 hr + 20 min
= 1 hr + 1/3 hr
= 4/3 hr
Let speeds be x and y .
Distance = speed × time
⇒ Distance = distance of A - distance of B
⇒ 80 = 8 x - 8 y
⇒ x - y = 10 .......( 1 )
If they travel in same directions :
Distance of both cars added gives 80 km .
4/3 x + 4/3 y = 80
⇒ 4/3 ( x + y ) = 80
⇒ x + y = 80 × 3/4
⇒ x + y = 60 .......( 2 )
Add 1 and 2 to get :
2 x = 70
= x = 70/2
= x = 35
x - y = 10
= 35 - y = 10
= y = 35 - 10
= y = 25
Hence speed of first car = 35 km/hr .
Speed of second car is 25 km/hr .
Step-by-step explanation:
When the cars start from the A and from B and they are travelling the same direction , the distance travelled by both will be different when they meet .
This distance can be calculated by subtracting the distance travelled by the car with the highest speed and the car with the lowest speed .
Whenever the car will travel towards each other , then the sum of the distances will be 80 km .