Number of hours after which the second person moves ahead of the first person if they travel at a given speed
Given three integers A, B and K. Initially, the first person was ahead of the second person by K kms. In every hour, the first person moves ahead by A kms and the second person moves ahead by B kms. The task is to print the number of hours after which the second person crosses the first. If it is impossible to do so then print -1.
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Input: A = 4, B = 5, K = 1
Initially, the first person was ahead by 1 km.
After 1st hour the first and second person are at the same place.
After 2nd hour the first person moves ahead of the first person by 1 km.
Input: A = 6, B = 5, K = 1
A naive approach is to linearly check for every hour and print the n-th hour when the second person moves ahead of the first person.
An efficient approach is to solve the problem mathematically. The number of hours will be K / (B – A) + 1 when the second person moves ahead of the first person. Since you need to cover K kms, hence the time taken will be K / (B – A) where B – A is the speed of the second person with respect to the first person. If A ≥ B then it is not possible for the second person to cross the first person.
Below is the implementation of the above approach: