Question

Из пункта А в пункт В, расстояние между которыми 50км, одновременно выехали автомобилист и велосипедист. Известно, что в час автомобилист проезжает на 65км больше, чем велосипедист. Определите скорость велосипедиста, если известно, что он прибыл в пункт В на 4часа 20 минут позже автомобилиста. Ответ дайте вкм/ч.

Answer 1

Хкм/ч скорость велосипедиста,время 50/хч
х+65км/ч скорость автомобилиста,время 50/(х+65)ч
50/х-50/(х+65)=13/3
13х(х+65)-3*50*(х+65-х)=0
13х²+845х-9750=0
х²+65х-750=0
х1+х2=-65 и х1*х2=-750
х1=-75 не удов усл
х2=10км/ч скорость велосипедиста

Answer 2

Problem Analysis

We are given that a car and a cyclist simultaneously traveled from point A to point B, which are 50 km apart. The car travels 65 km/h faster than the cyclist. We need to determine the speed of the cyclist if we know that the cyclist arrived at point B 4 hours and 20 minutes later than the car.

Solution

Let's assume the speed of the cyclist is v km/h. Since the car travels 65 km/h faster than the cyclist, the speed of the car is v + 65 km/h.

We can use the formula distance = speed × time to calculate the time taken by each of them to travel from point A to point B.

The time taken by the cyclist is given by: time taken by cyclist = distance / speed of cyclist

The time taken by the car is given by: time taken by car = distance / speed of car

We know that the time taken by the cyclist is 4 hours and 20 minutes longer than the time taken by the car. We can convert 4 hours and 20 minutes to hours by dividing by 60: 4 hours and 20 minutes = (4 × 60 + 20) minutes = 260 minutes = 260 / 60 hours = 4.33 hours

So, we have the equation: time taken by cyclist = time taken by car + 4.33 hours

Substituting the values, we get: distance / speed of cyclist = distance / speed of car + 4.33

Since the distance is the same for both, we can cancel it out: 1 / speed of cyclist = 1 / speed of car + 4.33

Now, let's substitute the values for the speed of the car and solve for the speed of the cyclist.

Calculation

Let's substitute the values into the equation and solve for the speed of the cyclist:

1 / v = 1 / (v + 65) + 4.33

To solve this equation, we can multiply both sides by v(v + 65) to eliminate the fractions:

v(v + 65) / v = v(v + 65) / (v + 65) + 4.33(v + 65)

Simplifying the equation:

v + 65 = v + 65 + 4.33v + 282.45

Combining like terms:

v + 65 = 5.33v + 347.45

Subtracting v from both sides:

65 = 4.33v + 347.45

Subtracting 347.45 from both sides:

-282.45 = 4.33v

Dividing both sides by 4.33:

v ≈ -65.26

Since speed cannot be negative, we discard this solution.

Answer

Based on the calculations, we find that the speed of the cyclist is approximately -65.26 km/h. However, since speed cannot be negative, this solution is not valid.

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