Advertisements
Advertisements
Question
Two pipes running together can 1 fill a cistern in 11 1/9 minutes. If one pipe takes 5 minutes more than the other to fill the cistern find the time when each pipe would fill the cistern.
Advertisements
Solution
Let x minutes be time taken by the larger pipe to fill the cistern then the smaller pipe taken (x + 5) minutes. These two pipes would fill `(1)/x` and `(1)/(x + 5)` of the cistern in a minute, respectively.
`(1)/x + (1)/(x + 5) = (9)/(100)`
⇒ 9x2 - 155x - 500 = 0
⇒ 9x2 + 25x - 180x - 500 = 0
⇒ x (9x + 25) -20 (9x + 25) = 0
⇒ (9x + 25) (x - 20) = 0
⇒ x - 20 = 0
and 9x + 25 = 0
x = 20
and x = `-(25)/(9)` ...(negligible)
Hence the time taken by the pipes to fill the cistern in 20 minutes and 25 minutes.
RELATED QUESTIONS
Solve for x
:`1/((x-1)(x-2))+1/((x-2)(x-3))=2/3` , x ≠ 1,2,3
The sum of two numbers is 8 and 15 times the sum of their reciprocals is also 8. Find the numbers.
Solve the following quadratic equations by factorization: \[\frac{x - 4}{x - 5} + \frac{x - 6}{x - 7} = \frac{10}{3}; x \neq 5, 7\]
Solve the following quadratic equations by factorization: \[\frac{2}{x + 1} + \frac{3}{2(x - 2)} = \frac{23}{5x}; x \neq 0, - 1, 2\]
Find the value of p for which the quadratic equation
\[\left( p + 1 \right) x^2 - 6(p + 1)x + 3(p + 9) = 0, p \neq - 1\] has equal roots. Hence, find the roots of the equation.
Disclaimer: There is a misprinting in the given question. In the question 'q' is printed instead of 9.
If the equation 9x2 + 6kx + 4 = 0 has equal roots, then the roots are both equal to
The sum of a number and its reciprocal is `2 9/40`. Find the number.
A two digit number is such that the product of its digit is 8. When 18 is subtracted from the number, the digits interchange its place. Find the numbers.
In each of the following determine whether the given values are solutions of the equation or not
2x2 - 6x + 3 = 0; x = `(1)/(2)`
The speed of a boat in still water is 11 km/ hr. It can go 12 km up-stream and return downstream to the original point in 2 hours 45 minutes. Find the speed of the stream
