Two taps running together can fill a tank in 3$\frac{1}{13}$ hours
Quadratic Equations (10)Two taps running together can fill a tank in 3$\frac{1}{13}$ hours. If one tap takes 3 hours more than the other to fill the tank, then how much time will each tap take to fill the tank ?
Answer
Let one tap fill the tank in x hrs. Therefore, other tap fills the tank in (x + 3) hrs.
Work done by both the taps in one hour is
$$ \frac{1}{x} +\frac{1}{x+3} = \frac{13}{40} $$
(2x + 3) 40 = 13(x2 + 3x)
13x2 - 41x - 120 = 0
(13x + 24)(x - 5) = 0
x = 5
(rejecting the negative value)
Hence one tap takes 5 hrs and another 8 hrs separately to fill the tank.
Exam Year:
2017
Related Questions
- A train travels at a certain average speed for a distance of 63 km and then travels at a distance of 72 km
- Find the value of p, for which one root of the quadratic equation $px^2 - 14x + 8 = 0$ is 6 times the other
- Solve for x: $\frac{1}{x+1} +\frac{3}{5x+1} = \frac{5}{x+4}, x\ne-1, -\frac{1}{5}, -4$
- If ad $\ne$ bc, then prove that the equation
- Find the nature of roots of the quadratic equation $2x^2 – 4x + 3 = 0$
- Find the roots of the quadratic equation $x^2 − x − 2 = 0 $