Question

Два велосипедиста одновременно отправляются в 60 километровый пробег.первый едет со скоростью на 10 км/час большей,чем второй,прибывает к финишу на 3 часа раньше второго.найдите скорость велосипедиста,прибывшего к финишу первым

Answer 1

Х-скорость 1,х-10-скорость 2
60/(х-10)-60/х=3
60*х-60*(х-10)=3х(х-10)
60(х-х+10)=3х²-30х
3х²-30х-600=0
х²-10х-200=0
х1+х2=10 и х1*х2=-200
х1=20-скорость 1
х2=-10-не удов усл
20-10=10-скорость 2

Answer 2

Problem Analysis

Two cyclists start a 60-kilometer race simultaneously. The first cyclist rides at a speed 10 km/h faster than the second cyclist and finishes 3 hours earlier than the second cyclist. We need to find the speed of the cyclist who finishes first.

Solution

Let's denote the speed of the first cyclist as x km/h and the speed of the second cyclist as y km/h.

We have two pieces of information: 1. The first cyclist rides 10 km/h faster than the second cyclist: x = y + 10. 2. The first cyclist finishes 3 hours earlier than the second cyclist: 60/x = 60/y + 3.

We can use these two equations to solve for the speed of the first cyclist.

Calculation

From the first piece of information, we can express y in terms of x: y = x - 10.

Substitute y = x - 10 into the second equation: 60/x = 60/(x-10) + 3.

Now, we can solve for x.

Solving for x

To solve the equation 60/x = 60/(x-10) + 3 for x, we can follow these steps:

1. Multiply both sides by x(x-10) to clear the fractions. 2. Rearrange the equation to form a quadratic equation. 3. Solve the quadratic equation to find the value of x.

Let's proceed with the calculation.