Question

Мотоциклист должен преодолеть расстояние от города А до города Б за определённое время. Через два часа после того как он выехал, он заметил, что он преодолел 80 км, и если он будет продолжать двигаться с такой же скоростью, он прибудет в город Б с опозданием на 15 минут. Поэтому увеличил скорость на 10 км/ч, и прибыл в город B на 36 минут раньше запланированного времени. Найдите: а) Расстояние между двумя городами;b) Время, за которое мотоциклист должен был проехать от города A к городу B. Пж оч срочно, не дано решать такие задачи, друзья, математичка оч злая ​

Answer 1

Обозначим расстояние от А до Б в х км. Мотоциклист за первые два час проехал 80 км, поэтому его скорость была равна V = 80/2 = 40 км/ч. С такой скоростью он преодолел бы все расстояние за x/40 часов, опоздав на 15 минут, то есть точное время составило бы x/40 - 15/60 часов. Оставшийся путь (х - 80) км он проехал со скоростью V = 40 + 10 = 50 км/ч

. Поэтому, время, за которое он проехал полное расстояние от А до В составило: 2 + (х - 80)/50 часов и это на 36 мин. раньше, чем ожидалось. Поэтому запланированное время было: 2 + (х -80)/ 50 + 36/60 Когда мы приравняем выражения для ожидаемого времени, мы получим уравнение:

x/40 – 15/60 = 2 + (x -80)/50 + 36/60 <=> (x - 10)/40 = (100 + x - 80 + 30)/50 <=> (x - 10)/4 = (x +50)/5 <=> 5x - 50 = 4x + 200 <=> x = 250

Итак, искомое расстояние равно 250 км. Время возможно найти, заменив x на 250 в первом выражении, например:

x/40 – 15/60 = 250/40 – 1/4 = 25/4 – 1/4 = 24/4 = 6 часов.

Answer 2

#### Problem Analysis We are given the following information: - A motorcyclist travels from city A to city B. - After two hours of travel, the motorcyclist notices that they have covered 80 km. - If the motorcyclist continues at the same speed, they will arrive in city B 15 minutes late. - The motorcyclist increases their speed by 10 km/h and arrives in city B 36 minutes earlier than planned. We need to find: a) The distance between the two cities. b) The time it takes for the motorcyclist to travel from city A to city B. #### Solution Let's assume the initial speed of the motorcyclist is **v** km/h. We can calculate the distance between the two cities using the formula: **Distance = Speed × Time**. After two hours of travel, the motorcyclist has covered 80 km. Therefore, we can write the equation: **80 = v × 2**. If the motorcyclist continues at the same speed, they will arrive in city B 15 minutes late. Let's denote the total time taken to travel from city A to city B at the initial speed as **t** hours. We can write the equation: **Distance = Speed × Time = v × t**. Since the motorcyclist arrives 15 minutes late, the total time taken is **t + 15/60** hours. We can write the equation: **Distance = Speed × Time = v × (t + 15/60)**. The motorcyclist increases their speed by 10 km/h and arrives in city B 36 minutes earlier than planned. Let's denote the new speed as **v + 10** km/h. The total time taken to travel from city A to city B at the increased speed is **t - 36/60** hours. We can write the equation: **Distance = Speed × Time = (v + 10) × (t - 36/60)**. Now we have two equations with two unknowns (v and t). We can solve these equations to find the distance and time. #### Calculation Let's solve the equations step by step. From the equation **80 = v × 2**, we can solve for v: **v = 80/2 = 40** km/h. Using the equation **Distance = Speed × Time = v × t**, we can find the distance between the two cities: **Distance = 40 × t**. Using the equation **Distance = Speed × Time = v × (t + 15/60)**, we can find another expression for the distance: **Distance = 40 × (t + 15/60) = 40t + 10**. Using the equation **Distance = Speed × Time = (v + 10) × (t - 36/60)**, we can find another expression for the distance: **Distance = (40 + 10) × (t - 36/60) = 50t - 30**. Since all expressions represent the same distance, we can equate them: **40t + 10 = 50t - 30**. Simplifying the equation, we get: **10t = 40**. Solving for t, we find: **t = 4** hours. Now, we can find the distance between the two cities: **Distance = 40 × t = 40 × 4 = 160** km. #### Answer a) The distance between the two cities is **160 km**. b) The time it takes for the motorcyclist to travel from city A to city B is **4 hours**. Please note that the calculations are based on the given information and assumptions made during the problem analysis.