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

| July 25, 2021 | education

From points A and B, the distance between which is 19 km, two tourists left at the same time towards each other and met 9 km from point A. Find the speed of the tourist leaving point A, if it is known that he was walking at a speed of 1 km / h more than another tourist and made the 30 minute pass.

Let x km / h be the speed of the first tourist leaving A, then (x – 1) km / h is the speed of the second. The distance from A to B is 19 km, the meeting took place 9 km from A, which means the second traveled 19 – 9 = 10 km. The first was 9 / x h, the second – 10 / (x – 1) h. It is known that a tourist who left A had a rest for 1/2 h.

9 / x + 1/2 = 10 / (x – 1).

Let’s bring to a common denominator.

9 * 2 (x -1) + x (x – 1) = 10 * 2x,

18x – 18 + x ^ 2 – x = 20x,

x ^ 2 – 3x – 18 = 0,

D = 9 + 4 * 18 = 81 = 92.

x1,2 = (3 + 9) / 2.

Positive root x = 6.

Answer: 6 km / h.



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