Question

4.3 пункту А спочатку виїхав перший велосипедист, а через 15 хвилин у тому ж напрямі виїхав другий зі швидкістю у 1,2 рази більшою від швидкості першо- го, і наздогнав його на відстані 45 км від А. Знайти швидкість першого вело- сипедиста.

Answer 1

To find the speed of the first cyclist, we can use the formula:

Speed = Distance / Time

Let's break down the information given in the question:

- The first cyclist started first. - After 15 minutes (or 0.25 hours), the second cyclist started. - The second cyclist's speed is 1.2 times greater than the speed of the first cyclist. - The second cyclist catches up to the first cyclist at a distance of 45 km from point A.

Calculating the Speed of the First Cyclist:

Let's assume the speed of the first cyclist is x km/h.

The second cyclist's speed is 1.2 times greater, so the speed of the second cyclist is 1.2x km/h.

Now, let's calculate the time it takes for the second cyclist to catch up to the first cyclist.

The first cyclist has been cycling for 15 minutes, which is equivalent to 0.25 hours.

The second cyclist catches up to the first cyclist after a certain time, let's call it t hours.

During this time, the first cyclist travels a distance of x * t km.

The second cyclist travels a distance of 1.2x * t km.

According to the question, the second cyclist catches up to the first cyclist at a distance of 45 km from point A.

Therefore, we can set up the following equation:

x * t + 45 = 1.2x * t

Simplifying the equation:

0.2x * t = 45

Now, we need to find the value of t.

Dividing both sides of the equation by 0.2x:

t = 45 / (0.2x)

Since we know that the first cyclist has been cycling for 0.25 hours before the second cyclist starts, we can add this time to t:

t + 0.25 = 45 / (0.2x) + 0.25

Now, we can solve this equation to find the value of x.

Please note that the equation involves a variable in the denominator, so we need to be careful when solving it.