Two motor cyclists meet after 2 hours if they drive from 100 km apart in the…
2023
Two motor cyclists meet after 2 hours if they drive from 100 km apart in the same direction , but they meet in 1 hour if they drive in the opposite direction . The ratio between the speed of faster motor cyclist and the other one is :
- A.
2:1
- B.
3:1
- C.
3:2
- D.
4:2
Attempted by 2 students.
Show answer & explanation
Correct answer: B
Answer: 3:1
Let the speed of the faster motorcyclist be A and the slower be B.
When they travel in the same direction, the relative speed is A - B. They meet after 2 hours, so 100 = (A - B) × 2 ⇒ 2A - 2B = 100.
When they travel in opposite directions, the relative speed is A + B. They meet after 1 hour, so 100 = (A + B) × 1 ⇒ A + B = 100.
Both right-hand sides equal 100, so set the left-hand sides equal: 2A - 2B = A + B. Rearranging gives A = 3B.
Substitute A = 3B into A + B = 100 ⇒ 3B + B = 100 ⇒ 4B = 100 ⇒ B = 25 and A = 75.
Therefore the ratio of the faster to the slower motorcyclist is A:B = 75:25 = 3:1.