5139. Average train speed

Find the average speed of the train, if it traveled the first half of the distance at a speed of v₁, and the second half at a speed of v₂.

Input. Two integers v₁ and v₂ (1 ≤ v₁, v₂ ≤ 10⁹).

Output. Print the average speed of the train with 4 decimal places.

Sample input 1	Sample output 1
10 10	10.0000
Sample input 2	Sample output 2
50 100	66.6667

SOLUTION

mathematics

Algorithm analysis

Let s be the distance traveled by the train.

The train will cover the first half of the distance in time = .

The train will cover the second half of the distance in time = .

The time it takes for the train to cover the entire distance is equal to

s / (2v₁) + s / (2v₂)

Then the average speed of the train equals the length of the path divided by the time taken to cover that path, which is

v_average = = =

Algorithm realization

Read the input data.

scanf("%lf %lf",&v1,&v2);

Compute and print the average speed.

ave = 2 * v1 * v2 / (v1 + v2);

printf("%.4lf\n",ave);