Question

Прошу помогите решить очень нужно Два бе­гу­на од­но­вре­мен­но стар­то­ва­ли в одном на­прав­ле­нии из од­но­го и того же места кру­го­вой трас­сы в беге на не­сколь­ко кру­гов. Спу­стя один час, когда од­но­му из них оста­ва­лось 3 км до окон­ча­ния пер­во­го круга, ему со­об­щи­ли, что вто­рой бегун прошёл пер­вый круг 6 минут назад. Най­ди­те ско­рость пер­во­го бе­гу­на, если из­вест­но, что она на 5 км/ч мень­ше ско­ро­сти вто­ро­го.

Answer 1

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Answer 2

Problem Analysis

We have two runners who start simultaneously from the same point on a circular track and run for several laps. After one hour, when one of the runners has 3 km left to complete the first lap, they are informed that the second runner completed the first lap 6 minutes ago. We need to find the speed of the first runner, given that it is 5 km/h slower than the speed of the second runner.

Solution

Let's assume the speed of the second runner is x km/h. According to the problem, the speed of the first runner is 5 km/h slower, so it is (x - 5) km/h.

To solve this problem, we need to find the time it takes for each runner to complete one lap. We can then use this information to find the speed of the first runner.

Let's calculate the time it takes for the second runner to complete one lap. We know that the second runner completed the first lap 6 minutes ago, which means they took 60 minutes + 6 minutes = 66 minutes to complete one lap.

Now, let's calculate the time it takes for the first runner to complete one lap. We know that the first runner has 3 km left to complete the first lap after one hour. Since the speed of the first runner is (x - 5) km/h, we can calculate the time it takes for the first runner to cover 3 km using the formula:

Time = Distance / Speed

Substituting the values, we get:

Time = 3 km / (x - 5) km/h

Now, we can set up an equation to solve for x:

66 minutes = Time taken by the second runner to complete one lap = Time taken by the first runner to cover 3 km

Converting 66 minutes to hours, we get:

66 minutes = 66/60 hours = 11/10 hours

Substituting the values, we get:

11/10 hours = 3 km / (x - 5) km/h

To solve for x, we can cross-multiply and solve the resulting equation:

11(x - 5) = 10(3)

Simplifying the equation, we get:

11x - 55 = 30

11x = 85

x = 85/11

Therefore, the speed of the second runner is approximately 7.73 km/h.

Since the speed of the first runner is 5 km/h slower, the speed of the first runner is approximately (7.73 - 5) = 2.73 km/h.

Answer

The speed of the first runner is approximately 2.73 km/h.