Question

на путь равный 18 км, велосипедист затратил времени на 1 ч 48 мин меньше, чем пешеход, так как проезжал за 1 ч на 9 км больше, чем проходил пешеход. Каковы скорости велосипедиста и пешехода?

Answer 1

пусть скорость пешехода-х,тогда велосепидиста х+9.Из условия:

18:х-1,8=18*(х+9)

10:х-1=10:(х+9)

10(х+9)-х(х+9)=10х

90-х*х-9х=0

x^2+9x-90=0

D=81+360=441

x=(-9+-21)/2

x>0=>x=6км:ч-скорость пешехода

6+9=15км:ч-скорость велосепедиста

Answer 2

Problem Analysis

We are given that a cyclist traveled a distance of 18 km in 1 hour and 48 minutes less time than a pedestrian. Additionally, the cyclist traveled 9 km more than the pedestrian in the same amount of time. We need to determine the speeds of both the cyclist and the pedestrian.

Solution

Let's assume the speed of the pedestrian is x km/h. Therefore, the speed of the cyclist would be x + 9 km/h since the cyclist traveled 9 km more than the pedestrian in the same amount of time.

To calculate the time taken by the pedestrian, we can use the formula time = distance / speed. The distance traveled by the pedestrian is 18 km, and the speed is x km/h. Therefore, the time taken by the pedestrian is 18 / x hours.

Similarly, the time taken by the cyclist is 18 km, and the speed is x + 9 km/h. Therefore, the time taken by the cyclist is 18 / (x + 9) hours.

According to the problem, the cyclist took 1 hour and 48 minutes less time than the pedestrian. We can convert 1 hour and 48 minutes to hours by dividing it by 60. Therefore, the time difference is 1 + 48/60 hours.

Now we can set up an equation using the time taken by the cyclist and the pedestrian:

18 / (x + 9) = 18 / x - (1 + 48/60)

Let's solve this equation to find the value of x.

Calculation

To solve the equation, we can start by cross-multiplying:

18x = 18(x + 9) - (1 + 48/60)(x + 9)

Simplifying the equation:

18x = 18x + 162 - (1 + 48/60)x - (1 + 48/60) * 9

Simplifying further:

18x = 18x + 162 - x - 9 - (48/60)x - (48/60) * 9

Combining like terms:

18x - 18x + x + (48/60)x = 162 - 9 - (48/60) * 9

Simplifying:

x(1 + 48/60) = 162 - 9 - (48/60) * 9

Calculating the right side of the equation:

x(1 + 48/60) = 162 - 9 - (48/60) * 9

x(1 + 48/60) = 162 - 9 - 36

x(1 + 48/60) = 117

Dividing both sides by (1 + 48/60):

x = 117 / (1 + 48/60)

Calculating the right side of the equation:

x = 117 / (1 + 48/60)

x = 117 / (1 + 4/5)

x = 117 / (9/5)

x = 117 * (5/9)

x = 65

Therefore, the speed of the pedestrian is 65 km/h.

Since the speed of the cyclist is x + 9, the speed of the cyclist is 65 + 9 = 74 km/h.

Answer

The speed of the pedestrian is 65 km/h, and the speed of the cyclist is 74 km/h.