?a motorcyclist and a car movea in opposite directions after 2 hours t...
Given information:
- After 2 hours, the distance between the motorcyclist and the car is 140 km when they move in opposite directions.
- If they had traveled in the same direction, the distance between them would have been 20 km after 2 hours.
To find:
- Speed of the car
- Speed of the motorcyclist
Assumptions:
- The speeds of both the car and the motorcyclist are constant throughout the journey.
- The distance traveled by both the car and the motorcyclist in 2 hours is the same regardless of their directions.
Solution:
Step 1: Understanding the situation
- Let's assume the speed of the car is "C" km/h and the speed of the motorcyclist is "M" km/h.
- When they move in opposite directions, their speeds are added, so the relative speed between them is (C + M) km/h.
- When they move in the same direction, their speeds are subtracted, so the relative speed between them is (C - M) km/h.
Step 2: Calculating the distance traveled in both cases
- After 2 hours, the distance traveled by the car and the motorcyclist when moving in opposite directions is (C + M) * 2 km.
- After 2 hours, the distance traveled by the car and the motorcyclist when moving in the same direction is (C - M) * 2 km.
Step 3: Solving the equations
- According to the given information, (C + M) * 2 = 140 km (when moving in opposite directions).
- According to the given information, (C - M) * 2 = 20 km (when moving in the same direction).
Step 4: Solving the equations to find the speeds
- From the first equation, we can rewrite it as C + M = 70 km/h.
- From the second equation, we can rewrite it as C - M = 10 km/h.
- Adding both equations, we get 2C = 80 km/h.
- Dividing both sides by 2, we find C = 40 km/h.
- Substituting the value of C in either of the equations, we find M = 30 km/h.
Step 5: Conclusion
- The speed of the car is 40 km/h, and the speed of the motorcyclist is 30 km/h.
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