From points A and B, the distance between which is 19 km, 2 pedestrians left at the same time towards

From points A and B, the distance between which is 19 km, 2 pedestrians left at the same time towards each other and met 9 km from point A. Find the speed of each, if it is known that the pedestrian leaving A. walked at a speed of 1 km / more than another pedestrian and made a 30-minute stop on the way

Since pedestrians met 9 km from point A, the second pedestrian, therefore, passed:

19 – 9 = 10 km.

Let’s say that his speed is x km / h, so he was on the way for 10 / x hours.

The speed of the first pedestrian was 1 km / h more, that is, equal to x +1 km / h and he covered 9 km in 9 / (x + 1) hours, taking into account a stop for 30 minutes or 1/2 hour.

Let’s compose and solve the equation:

9 / (x + 1) + 1/2 = 10 / x,

(18 + x + 1) / (2 * x + 2) = 10 / x,

19 * x + x² = 20 * x + 20,

x² – x – 20 = 0.

The discriminant of this equation is:

(-1) ² – 4 * 1 * (-20) = 81.

Since x can only be a positive number, the equation has a unique solution:

x = (1 + 9) / 2 = 5 (km / h) – speed of the second cyclist.

5 + 1 = 6 (km / h) – the speed of the first cyclist.