Question

Первый велосипедист проходит трассу на 3 мин быстрее второго и догоняет второго каждые полтора часа. За какое время первый велосипедист прозодит трассу?

Answer 1

Тебе по действиям. Или как

Answer 2

Problem Analysis

We are given that the first cyclist completes the route 3 minutes faster than the second cyclist and catches up to the second cyclist every 1.5 hours. We need to find the time it takes for the first cyclist to complete the route.

Solution

Let's assume that the time taken by the second cyclist to complete the route is x hours.

According to the given information, the first cyclist completes the route 3 minutes faster than the second cyclist. So, the time taken by the first cyclist to complete the route is x - 3 hours.

We are also given that the first cyclist catches up to the second cyclist every 1.5 hours. This means that in 1.5 hours, the second cyclist covers the same distance that the first cyclist covers in x - 3 hours.

To find the time taken by the first cyclist to complete the route, we can set up the following equation:

Distance covered by the second cyclist in 1.5 hours = Distance covered by the first cyclist in (x - 3) hours

Let's solve this equation:

Distance = Speed * Time

The speed of both cyclists is the same, as they are traveling on the same route. So, we can cancel out the speed from both sides of the equation.

Distance covered by the second cyclist in 1.5 hours = Distance covered by the first cyclist in (x - 3) hours

Let's assume the distance of the route is d.

So, we have:

(d / x) * 1.5 = (d / (x - 3)) * (x - 3)

Simplifying the equation:

1.5x = d

Now, we need to find the value of x.

From the given search snippet, we can see that the equation simplifies to:

560 * (x + 10) - 560 * x = 70 * (x + 10) - 80 * x

Simplifying further:

560x + 5600 - 560x = 70x + 700 - 80x

5600 = -10x + 700

-10x = 700 - 5600

-10x = -4900

x = -4900 / -10

x = 490

Therefore, the second cyclist takes 490 hours to complete the route.

To find the time taken by the first cyclist, we subtract 3 minutes (or 3/60 hours) from the time taken by the second cyclist:

Time taken by the first cyclist = 490 - 3/60

Calculating the result:

Time taken by the first cyclist = 490 - 0.05

Time taken by the first cyclist = 489.95 hours

Answer

The first cyclist takes approximately 489.95 hours to complete the route.

Please note that the given search snippet does not provide the complete context for the problem, so the calculations and assumptions made in this response are based on the available information.