Question

Гоночный автомобиль ехал из пункта А в пункт В со скоростью 180км/ч. Если бы его скорость была 200км/ч, то на путь АВ ушло бы на 30 мин меньше. Найдите АВ.

Answer 1

Примем расстояние АВ за S км, тогда: путь со скоростью 180 км/час автомобиль пройдет за время: S/180 = t; а со скоростью 200 км/час, за время (t-0,5)час или (t-1/2)час. Вычтем второе выражение из первого: S/180 -S/200 =1/2;  10S/1800 - 9S/1800 = 900/1800;   S = 900 (км)

Answer 2

Calculation of Distance (AB)

To find the distance between points A and B, we need to use the information given in the question. Let's assume that the original speed of the racing car is 180 km/h, and if its speed were 200 km/h, it would take 30 minutes less to travel from A to B.

Let's denote the distance between A and B as AB.

We can use the formula: time = distance / speed.

At the original speed of 180 km/h, the time taken to travel from A to B is AB / 180.

If the speed were 200 km/h, the time taken to travel from A to B would be AB / 200.

According to the question, the difference in time is 30 minutes, which is equal to 0.5 hours.

Therefore, we can set up the equation:

AB / 180 - AB / 200 = 0.5

To solve this equation, we can find a common denominator and simplify:

(200 * AB - 180 * AB) / (180 * 200) = 0.5

20 * AB / (180 * 200) = 0.5

20 * AB = 0.5 * 180 * 200

20 * AB = 180 * 100

AB = (180 * 100) / 20

AB = 900

Therefore, the distance between points A and B (AB) is 900 kilometers.