Question

Из двух пунктов, расстояние между которыми 104 1/2 км, одновременно навстречу друг другу выехали два велосипедиста. Скорость одного из них равна 18 км/ч, а другого - 20 км/ч. Через какого время они встретятся?

Answer 1

Problem Analysis

We have two cyclists who start simultaneously from two points that are 104 1/2 km apart. The first cyclist has a speed of 18 km/h, while the second cyclist has a speed of 20 km/h. We need to determine the time it takes for them to meet.

Solution

To solve this problem, we can use the formula: time = distance / speed.

Let's calculate the time it takes for each cyclist to cover the distance until they meet.

For the first cyclist: - Distance covered = 104 1/2 km - Speed = 18 km/h

Using the formula, we can calculate the time taken by the first cyclist: time1 = distance / speed = 104 1/2 km / 18 km/h.

For the second cyclist: - Distance covered = 104 1/2 km - Speed = 20 km/h

Using the formula, we can calculate the time taken by the second cyclist: time2 = distance / speed = 104 1/2 km / 20 km/h.

To find the total time taken for them to meet, we can add the individual times: total time = time1 + time2.

Let's calculate the values.

Calculation

First, let's convert 104 1/2 km to a decimal value: 104 1/2 km = 104.5 km.

Now, let's calculate the time taken by the first cyclist: time1 = 104.5 km / 18 km/h.

Using a calculator, we find that time1 ≈ 5.8056 hours.

Next, let's calculate the time taken by the second cyclist: time2 = 104.5 km / 20 km/h.

Using a calculator, we find that time2 ≈ 5.225 hours.

Finally, let's calculate the total time taken for them to meet: total time = time1 + time2.

Using a calculator, we find that total time ≈ 11.0306 hours.

Answer

The two cyclists will meet approximately 11.0306 hours after they start.

Please note that the above calculations are approximate and may vary slightly depending on the exact values used.