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प्रश्न
The distance between two places A and B on road is 70 kilometers. A car starts from A and the other from B. If they travel in the same direction, they will meet after 7 hours. If they travel towards each other they will meet after 1 hour, then find their speeds.
उत्तर
Let the speed of the faster car be x km/h and that of the slower car be y km/h.
Total distance between them is 70 km.
Speed = ` "Distance" / "Time"`
When both cars travel in the same direction, they meet in 7 hours.
Total speed = x − y
`x - y = 70/7`
⇒ x - y = 10 ...(I)
When both cars move towards each other,
Total speed = x + y
`x + y = 70/1`
⇒ x + y = 70 ...(II)
Adding (I) and (II)
x - y = 10
x + y = 70
2x = 80
⇒ x = 40
Putting the value of x in (I)
∴ x - y = 10
∴ 40 - y = 10
∴ y = 40 - 10
⇒ y = 30
∴ The speed of a car starting from A is 40 km/hr and the speed of a car starting from B is 30 km/hr.
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