Question

Из пункта А в пункт В,расстояние между которыми 60 км,одновременно выехали автомобилист и велосипедист.известно,что в час автомобилист проезжает на 35 км больше ,чем велосипедист.определите, скорость велосипедиста,если известно ,что он прибыл в пункт В на 2 часа 48 минут позже автомобилиста.ответ двйте а км/ч.

Answer 1

2 ч 48 мин=2 4/5 ч=14/5 ч (48:60=4/5)
х - скорость велосипеда
х+35 - скорость автомобиля
60/х - время велосипеда
60/(х+35) - время автомобиля
60/х-60/(х+35)=14/5  (умножим на 5х(х+35))
300(х+35)-300х=14х(х+35)  (сократим на 2)
150(х+35)-150х=7х(х+35)
150х+5250-150х=7х2+245х
7х2+245х-5250=0  (сократим на 7)
х2+35х-750=0
D=35*35-4(-750)=1225+3000=4225;   Корень из D=65
х"=(-35-65):2=-100:2=-50 (не подходит по условию)
х=(-35+65):2=30:2=15 (км/ч)
Ответ: скорость велосипедиста 15 км/ч

Answer 2

Problem Analysis

We are given that the distance between point A and point B is 60 km. An automobile driver and a cyclist simultaneously start their journey from point A to point B. It is known that the automobile driver travels 35 km/h faster than the cyclist. We need to determine the speed of the cyclist if we know that the cyclist arrives at point B 2 hours and 48 minutes later than the automobile driver.

Solution

Let's assume the speed of the cyclist is x km/h. Since the automobile driver travels 35 km/h faster, their speed will be x + 35 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 automobile driver is given by: time taken by automobile driver = distance / speed of automobile driver

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

We are given that the cyclist arrives at point B 2 hours and 48 minutes later than the automobile driver. We need to convert this time to hours. 2 hours and 48 minutes is equal to 2 + 48/60 = 2.8 hours.

Using the above information, we can set up the following equation: time taken by automobile driver - time taken by cyclist = 2.8 hours

Substituting the values, we get: (distance / (x + 35)) - (distance / x) = 2.8

Simplifying the equation, we get: ((distance * x) - (distance * (x + 35))) / (x * (x + 35)) = 2.8

Simplifying further, we get: (60 * x) - (60 * (x + 35)) = 2.8 * x * (x + 35)

Simplifying again, we get: 60x - 60(x + 35) = 2.8x(x + 35)

Solving this equation will give us the value of x, which is the speed of the cyclist.

Calculation

Let's solve the equation to find the speed of the cyclist.

60x - 60(x + 35) = 2.8x(x + 35)

Expanding the equation: 60x - 60x - 60 * 35 = 2.8x^2 + 2.8 * 35x

Simplifying: -60 * 35 = 2.8x^2 + 2.8 * 35x

-2100 = 2.8x^2 + 98x

Rearranging the equation: 2.8x^2 + 98x + 2100 = 0

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

where a = 2.8, b = 98, and c = 2100.

Calculating the values: x = (-98 ± √(98^2 - 4 * 2.8 * 2100)) / (2 * 2.8)

x = (-98 ± √(9604 - 23520)) / 5.6

x = (-98 ± √(-13916)) / 5.6

Since the discriminant is negative, the equation has no real solutions. This means that there is no valid speed for the cyclist that satisfies the given conditions.

Answer

There is no valid speed for the cyclist that satisfies the given conditions.