Advertisements
Advertisements
प्रश्न
The speed of a boat in still water is 8 km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.
उत्तर
Let the speed of stream be x km/hr then
Speed downstream = (8 + x)km/hr.
Therefore, Speed upstream = (8 - x)km/hr
Time taken by the boat to go 15km upstream `15/(8-x)hr`
Time taken by the boat to returns 22km downstream `22/(8+x)hr`
Now it is given that the boat returns to the same point in 5 hr.
So,
`15/(8-x)+22/(8+x)=5`
`(15(8+x)+22(8-x))/((8-x)(8+x))=5`
`(120+15x+176-22x)/(64-x^2)=5`
`(296-7x)/(64-x^2)=5`
5x2 - 7x + 296 - 320 = 0
5x2 - 7x - 24 = 0
5x2 - 15x + 8x - 24 = 0
5x(x-3) + 8(x - 3) = 0
(x - 3)(5x + 8) = 0
x - 3 = 0
x = 3
Or
5x + 8 = 0
5x = -8
x = -8/5
But, the speed of the stream can never be negative.
Hence, the speed of the stream is x = 3 km/hr
APPEARS IN
संबंधित प्रश्न
Solve for x: `(x-3)/(x-4)+(x-5)/(x-6)=10/3; x!=4,6`
Solve the following quadratic equations by factorization:
`a/(x-a)+b/(x-b)=(2c)/(x-c)`
The sum of two numbers is 48 and their product is 432. Find the numbers?
The sum of ages of a man and his son is 45 years. Five years ago, the product of their ages was four times the man's age at the time. Find their present ages.
The perimeter of a rectangular field is 82 m and its area is 400 m2. Find the breadth of the rectangle.
A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish the work.
For the equation given below, find the value of ‘m’ so that the equation has equal roots. Also, find the solution of the equation:
(m – 3)x2 – 4x + 1 = 0
Solve the following quadratic equations by factorization: \[\frac{16}{x} - 1 = \frac{15}{x + 1}; x \neq 0, - 1\]
The polynomial equation x(x + 1) + 8 = (x + 2) (x – 2) is:
Which of the following is correct for the equation `1/(x - 3) - 1/(x + 5) = 1`?
