From points A and B, the distance between which is 19 km, two pedestrians left at the same time towards

From points A and B, the distance between which is 19 km, two pedestrians left at the same time towards each other and met 9 km from A. Find the speed of the pedestrian walking from A, if it is known that he was walking at a speed 1 km / h more than the pedestrian walking from B, and made a half-hour stop on the way

First, use the equation to find the speed of the rider from B.

Let x be from point B.
Let x + 1 be from point A.

Let’s compose an equation and thus find the speed of going from A.

9: (x + 1) + 0.5 = 10 / x;
9: (x + 1) + 0.5 – 10 / x = 0;
9x + 0.5x * (x + 1) – 10 * (x + 1) = 0;
9x + 0.5×2 + 0.5x – 10x – 10 = 0;
0.5×2 – 0.5x – 1 0 = 0;
x2 – x – 20 = 0;

Next, we solve the problem through the discriminant.

D = 1 – 4 * (- 20) = 1 + 80 = 81 = 9;

x1 = 1 + 9/2 = 5 (km / h) – from V.
x2 = 1 – 9/2 = – 4 – does not satisfy.

It remains to find out the speed of the pedestrian from A.

5 + 1 = 6 (km / h) – from A.

Answer: the speed of a pedestrian from A is 6 km / h.