Two water pumps are filling a pool. One of the pumps is high power and can fill the pool 5 hours before the other can do. Howeve

Question

3 years ago

12

Two water pumps are filling a pool. One of the pumps is high power and can fill the pool 5 hours before the other can do. Howeve

r, they both working together can fill half of the pool in 3 hours. In how many hours the high power pump can fill the pool?

Mathematics

2 answers:

julsineya [31] · Answer 1 · 2021-11-13T08:03:48+03:00

julsineya [31]3 years ago

7 0

The answer is 2 hours u only subtract 3 hours from 5 hours. at least that what i say im not sure if im correct

belka [17] · Answer 2 · 2021-11-13T09:04:04+03:00

The time taken by the high power pump can fill the pool is $\boxed{4.4{\text{ hours}}}.$

Further explanation:

Given:

One of the pumps is high power and can fill the pool 5 hours before the other can do.

They both working together can fill half of the pool in 3 hours.

Explanation:

Consider the time taken by the slower pump be $x{\text{ hours}}.$

The taken by the high speed pump is $\left( {x - 5} \right){\text{ hours}}$ .

The amount of water filled in one hour by slower pump can be expressed as follows,

${t_1} = \dfrac{1}{x}$

The amount of water filled in one hour by slower pump can be expressed as follows,

${t_2} = \dfrac{1}{x-5}$

They both working together can fill half of the pool in 3 hours.

$\begin{aligned}\frac{1}{x} + \frac{1}{{x - 5}} &= \frac{1}{3}\\\frac{{x - 5 + x}}{{x\left( {x - 5} \right)}} &= \frac{1}{3}\\\frac{{2x - 5}}{{{x^2} - 5x}} &= \frac{1}{3}\\6x - 15 &= {x^2} - 5x\\0 &= {x^2} - 11x + 15\\\end{aligned}$

Solve the quadratic equation.

$\begin{aligned}x &= \frac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}\\x &= \frac{{ - \left( { - 11} \right) \pm \sqrt {{{\left( { - 11} \right)}^2} - 4\left( 1 \right)\left( {15} \right)} }}{{2 \times 1}} \\ x&= \frac{{11 \pm \sqrt {61} }}{2}\\x&= \frac{{11 + 7.8}}{2}{\text{ or }}x = \frac{{11 - 7.8}}{2}\\x &= 9.4{\text{ or }}x = 1.6\\\end{aligned}$