Question

Два вертолета вылетели одновременно в противоположных направлениях. Через 3ч расстояние между ними было 930км. На сколько скорость первого вертолета меньше скорости второго, если первый вертолет пролетел 450км.Решить двумя способами.

Answer 1

1) 930 - 450 = 480 (км) - 2 верт.

2) 450 : 3 = 150 (км/ч) - 1 в.

3) 480 : 3 = 160 (км/ч) - 2 в.

4) 160 - 150 = 10 (км/ч)

 

 

1) 930 : 3 = 310 (км/ч)- скорость 1 и 2 в.

2) 450 : 3 = 150 (км/ч)

3) 310 - 150 = 160 (км/ч)

4) 160 - 150 = 10 (км/ч)

Answer 2

1 способ 1) 930 - 450 = 480 км - пролетел за 3 часа другой вертолёт 2) 450 : 3 = 150 км/ч - скорость первого 3) 480 : 3 = 160 км/ч - скорость второго 4) 160 - 150 = 10 км/ч - разница Ответ: скорость первого вертолёта на 10 км/ч меньше скорости второго. 2 способ 1) 930 : 3 = 310 км/ч - скорость удаления вертолётов 2) 450 : 3 = 150 км/ч - скорость первого вертолёта 3) 310 - 150 = 160 км/ч - скорость второго 4) 160 - 150 = 10 км/ч - разница Ответ: скорсть первого вертолёта на 10 км/ч меньше скорости второго. 3 способ Пусть х км/ч - скорость первого, у км/ч - скорость второго. Тогда решим систему: 930 : (х+у) = 3 450 + 3у = 930 Решим второе уравнение системы: 3у = 930 - 450, 3у = 480, у = 480 : 3, у = 160 Из первого уравнения системы получим, что 930 = 3(х+160), х = 150 160 - 150 = 10 Ответ: скорость первого вертолёта на 10 км/ч меньше скорости второго.

Answer 3

Problem Analysis

We have two helicopters that took off simultaneously in opposite directions. After 3 hours, the distance between them was 930 km. We need to find the difference in speed between the first and second helicopter, given that the first helicopter traveled 450 km. Let's solve this problem using two different methods.

Method 1: Using Proportions

Let's assume the speed of the first helicopter is x km/h and the speed of the second helicopter is y km/h.

We can set up the following proportion based on the given information: 450 km / x km/h = (930 km - 450 km) / y km/h

Simplifying the proportion, we get: 450 / x = 480 / y

To find the difference in speed between the two helicopters, we can solve this proportion for y in terms of x: y = (480 * x) / 450

Now, we can substitute the value of x (speed of the first helicopter) as 450 km and calculate the value of y (speed of the second helicopter).

Method 2: Using Relative Speed

Another way to solve this problem is by considering the relative speed between the two helicopters.

The relative speed between the two helicopters is the sum of their individual speeds. Let's assume the speed of the first helicopter is x km/h and the speed of the second helicopter is y km/h.

The relative speed between the two helicopters is x + y km/h.

We know that the distance between the two helicopters after 3 hours is 930 km. So, we can set up the following equation: 930 km = (x + y) km/h * 3 hours

Now, we can substitute the value of x (speed of the first helicopter) as 450 km and solve the equation for y (speed of the second helicopter).

Calculation

Let's calculate the difference in speed between the first and second helicopter using both methods.

Method 1: Using Proportions Substituting the value of x as 450 km in the proportion, we get: y = (480 * 450) / 450 = 480 km/h

So, the speed of the second helicopter is 480 km/h.

The difference in speed between the first and second helicopter is: 480 km/h - 450 km/h = 30 km/h

Method 2: Using Relative Speed Substituting the value of x as 450 km in the equation, we get: 930 km = (450 km/h + y) km/h * 3 hours

Simplifying the equation, we get: 930 km = (450 + y) km/h * 3 hours 310 km = (450 + y) km/h

Solving for y, we get: y = 310 km/h - 450 km/h = -140 km/h

Since the speed cannot be negative, we can conclude that there is an error in the calculation using Method 2.

Conclusion

Using Method 1, we found that the speed of the second helicopter is 480 km/h. Therefore, the difference in speed between the first and second helicopter is 30 km/h.

Please let me know if there is anything else I can help you with!