Kitty cycles the first 350 km of a force and kilometre generator speed and average speed that is 15 km less than that for the first part of the general is taken the time for her travel part for her general is the same find the average speed for the second part of general
Let's assume the average speed for the first part of the journey is x km/h. Since Kitty cycles the first 350 km at this speed, the time it takes her is 350/x hours.
For the second part of the journey, let's assume the average speed is y km/h. Since the distance traveled is the same for the second part of the journey, the time it takes her is also 350/y hours.
According to the given information, the average speed for the second part of the journey is 15 km/h less than that for the first part. This can be written as y = x - 15.
Since the time for both parts of the journey is the same, we can equate the two time expressions:
350/x = 350/y
Cross multiplying this equation, we get:
y * 350 = x * 350
Substituting y = x - 15, we get:
(x - 15) * 350 = x * 350
Expanding the equation, we get:
350x - 5250 = 350x
Subtracting 350x from both sides, we get:
-5250 = 0
This equation has no solution.
Therefore, there is no average speed for the second part of the journey.
A man is 6 time as old as his son 20 years later the man will be twice as old as his son find the age of man when his son was born
Let's assume the current age of the son is x.
According to the problem, the man is 6 times as old as his son, so the current age of the man is 6x.
In 20 years, the son's age will be x + 20, and the man's age will be 6x + 20.
The problem states that in 20 years, the man will be twice as old as his son, so we can write the equation:
6x + 20 = 2(x + 20)
Simplifying the equation, we get:
6x + 20 = 2x + 40
Subtracting 2x from both sides, we get:
4x + 20 = 40
Subtracting 20 from both sides, we get:
4x = 20
Dividing both sides by 4, we get:
x = 5
Therefore, the current age of the son is 5.
To find the age of the man when his son was born, we need to subtract the son's age from the current age of the man:
6x - x = 5 * 6 - 5 = 30 - 5 = 25
So, the man was 25 years old when his son was born.
To find the average speed for the second part of the journey, we can use the formula:
Average Speed = Total Distance / Total Time
Given that Kitty cycles the first 350 km at a certain speed and the average speed for the first part of the journey is 15 km less than that, we can say:
Distance of first part = 350 km
Speed of first part = x km/h
Time taken for first part = distance / speed = 350 / x hours
Since the time for the second part is the same as that of the first part, we can set up the equation:
350 / x = time for second part
Let's call the distance for the second part "D" and the speed for the second part "y". The time for the second part is given by:
D / y = time for second part
Since the time for both parts is the same, we can set up the equation:
D / y = 350 / x
Now, to find the average speed for the second part, we need to find the total distance and total time for the journey.
Total Distance = Distance of first part + Distance of second part
Total Time = Time taken for first part (or Time taken for second part)
Total Distance = 350 + D
Total Time = 350 / x
Now, using the formula for average speed:
Average Speed = Total Distance / Total Time
Substituting the values, we have:
Average Speed = (350 + D) / (350 / x)
Since we know that the time for the second part is the same as the time for the first part, we can substitute D / y = 350 / x:
Average Speed = (350 + (x * 350 / y)) / (350 / x)
Simplifying the equation further:
Average Speed = (350y + 350x) / (350/y)
Average Speed = (350xy + 350x^2) / 350
Average Speed = xy + x^2
So, the average speed for the second part of the journey is xy + x^2 km/h.