SubwayTrip | Topcoder Archive

Problem Statement

You are walking down the escalator to catch a subway train. The escalator itself moves at a speed of Ve meters per minute. You can walk down the escalator at a relative speed of Vy meters per minute. The length of the escalator is L meters. Trains arrive T minutes apart.
Let t be the time between your arrival to the station if you stand still on the escalator and the arrival of the last train before your arrival. Assume that t is a random variable uniformly distributed between 0 and T.
Return the probability of catching an earlier train if you choose to walk down the escalator instead of standing still on it.

Definition

Class:: SubwayTrip
Method:: earlierTrain
Parameters:: int, int, int, int
Returns:: double
Method signature:: double earlierTrain(int Ve, int Vy, int L, int T)
(be sure your method is public)

Notes

The returned value must have an absolute or relative error less than 1e-9.

Constraints

Ve will be between 10 and 60, inclusive.
Vy will be between 1 and 10, inclusive.
L will be between 10 and 100, inclusive.
T will be between 2 and 20, inclusive.

Examples

```
10
```
```
10
```
```
20
```
```
2
```
```
Returns: 0.5
```
If you stand still, it'll take you 20/10 = 2 minutes to reach the bottom of the escalator. If you choose to walk, it'll make you 20/(10+10) = 1 minute. In the second case you save 1 minute and in 50% of the cases it'll allow you to catch an earlier train.
```
50
```
```
5
```
```
55
```
```
20
```
```
Returns: 0.005000000000000004
```
```
34
```
```
3
```
```
85
```
```
7
```
```
Returns: 0.028957528957528934
```
```
10
```
```
10
```
```
100
```
```
4
```
```
Returns: 1.0
```
Here, if you choose to walk instead of stand still, you will save 5 minutes and you will certainly be guaranteed to catch an earlier train.

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