Question

Два велосипедиста одновременно отправились в 140 километровый пробег.Первый ехал со скоростью, на 6 км/ч больше чем второй, и прибыл к финишу на 3 часа раньше второго .Найти скорость велосипедиста, пришедшего к финишу первым.

Answer 1

Пусть скорость первого х, тогда скорость второго х-6. Первый проехал 140 км за 140:х часов, второй - за 140: (х-6) часов. Разница во времени 140:(х-6) - 14:х = 3
Или 3 х^2 - 18 х +840 = 0
Решая уравнение, получаем два корня  20 и -14. Второй, очевидно, нам не подходит. Следовательно, скорсть первого велосипедиста 20км\час

Answer 2

Problem Analysis

We are given that two cyclists simultaneously started a 140-kilometer race. The first cyclist traveled at a speed 6 km/h faster than the second cyclist and arrived at the finish line 3 hours earlier than the second cyclist. We need to find the speed of the cyclist who finished first.

Solution

Let's assume the speed of the second cyclist is x km/h. Since the first cyclist traveled 6 km/h faster, their speed can be represented as x + 6 km/h.

We can use the formula distance = speed × time to calculate the time taken by each cyclist to complete the race.

For the first cyclist: - Distance = 140 km - Speed = x + 6 km/h - Time = 140 / (x + 6) hours

For the second cyclist: - Distance = 140 km - Speed = x km/h - Time = 140 / x hours

According to the problem, the first cyclist arrived at the finish line 3 hours earlier than the second cyclist. So, we can set up the following equation:

140 / (x + 6) = 140 / x + 3

Now, let's solve this equation to find the value of x.

Calculation

To solve the equation, we can cross-multiply and simplify:

140x = 140(x + 6) + 3x

Simplifying further:

140x = 140x + 840 + 3x

Combining like terms:

140x - 140x - 3x = 840

Simplifying further:

-3x = 840

Dividing both sides by -3:

x = -840 / 3

Simplifying further:

x = -280

Since speed cannot be negative, we can ignore the negative sign. Therefore, the speed of the second cyclist is 280 km/h.

To find the speed of the first cyclist, we can add 6 km/h to the speed of the second cyclist:

Speed of the first cyclist = 280 + 6 = 286 km/h

Therefore, the speed of the cyclist who finished first is 286 km/h.

Answer

The speed of the cyclist who finished first is 286 km/h.