Points 'A' and 'B' are 70 km apart on a highway and two cars start at the same…
2023
Points 'A' and 'B' are 70 km apart on a highway and two cars start at the same time. If they travel in the same direction, they meet in 7 hours, but if they travel towards each other they meet in one hour. Find the speed of the two cars (in km/hr).
- A.
20, 30
- B.
40, 30
- C.
30, 50
- D.
20, 40
Attempted by 2 students.
Show answer & explanation
Correct answer: B
Step-by-Step Solution
To find the speeds of the two cars, let their speeds be x km/hr and y km/hr, where x > y.
Case 1: Traveling in the same direction (Relative speed = x - y)
The cars are 70 km apart and meet in 7 hours.
Distance = Relative Speed × Time
70 = (x - y) × 7
x - y = 10 --- (Equation 1)
Case 2: Traveling towards each other (Relative speed = x + y)
The cars are 70 km apart and meet in 1 hour.
Distance = Relative Speed × Time
70 = (x + y) × 1
x + y = 70 --- (Equation 2)
Solve the equations:
Add Equation 1 and Equation 2: (x - y) + (x + y) = 10 + 70 2x = 80 x = 40 km/hr
Substitute x = 40 into Equation 2: 40 + y = 70 y = 30 km/hr
The speeds of the two cars are 40 km/hr and 30 km/hr.