Two water taps together can fill a tank in $9\frac{3}{8}$ hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Given:

Two water taps together can fill a tank in $9\frac{3}{8}$ hours. The tap of the larger diameter takes 10 hours less than the smaller one to fill the tank separately.

To do:

We have to find the time in which each tap can separately fill the tank.

Solution:

Time taken by both the taps to fill the tank$=9\frac{3}{8}=\frac{9\times8+3}{8}=\frac{72+3}{8}=\frac{75}{8}$ hours.

Let the time taken by the tap of the larger diameter to fill the tank be $x$ hours.

This implies,

The time taken by the tap of the smaller diameter to fill the tank$=x+10$ hours.

The portion of the tank filled by the larger tap in one hour $=\frac{1}{x}$.

The portion of the tank filled by the smaller tap in one hour $=\frac{1}{x+10}$.

The portion of the tank filled by both the taps in one hour $=\frac{1}{\frac{75}{8}}=\frac{8}{75}$.

Therefore,

$\frac{1}{x}+\frac{1}{x+10}=\frac{8}{75}$

$\frac{1(x+10)+1(x)}{(x+10)x}=\frac{8}{75}$

$\frac{x+10+x}{x^2+10x}=\frac{8}{75}$

$\frac{2x+10}{x^2+10x}=\frac{8}{75}$

$75(2x+10)=8(x^2+10x)$

$150x+750=8x^2+80x$

$8x^2+80x-150x-750=0$

$8x^2-70x-750=0$

$2(4x^2-35x-375)=0$

$4x^2-35x-375=0$

Solving for $x$ by factorization method, we get,

$4x^2-60x+25x-375=0$

$4x(x-15)+25(x-15)=0$

$(x-15)(4x+25)=0$

$x-15=0$ or $4x+25=0$

$x=15$ or $4x=-25$

Therefore, the value of $x=15$. ($x$ cannot be negative)

$x+10=15+10=25$

The time taken by the tap with larger diameter to fill the tank is $15$ hours and the time taken by the tap with smaller diameter is $25$ hours.

Related Articles

- Two water taps together can fill a tank in $9\frac{3}{8}$ hours. The tap of the larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
- Two pipes running together can fill a tank in $1\frac{7}{8}$ hours. The tap with longer diameter takes 2 hours less than the tap with the smaller one to fill the tank separately. Find the time in which each tap can fill the tank separately.
- 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 fil the tank ?
- Two pipes running together can fill a tank in $11\frac{1}{9}$ minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.
- To fill a swimming pool two pipes are used. If the pipe of larger diameter used for 4 hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled. Find, how long it would take for each pipe to fill the pool separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool?
- Two pipes running together can fill a cistern in $3\frac{1}{13}$ minutes. If one pipe takes $3$ minutes more than the other to fill it, find the time in which pipe nwould fill the cistern?
- The ratio of the time taken by tap A to fill the bathtub to that by tap B is 5: 6. If tap A takes 36 minutes to fill a bathtub, how long would B take to fill the same bathtub?
- If a tank is filled with $\frac{1}{3}$% of water and there are only 27 litres of water in the tank, what is the total capacity of tank?
- If two pipes function simultaneously, a reservoir will be filled in 12 hours. One pipe fills the reservoir 10 hours faster than the other. How many hours will the second pipe take to fill the reservoir?
- A water tank contains 6500 litre of water during transit to a nearby society. 3 by 16 of the water was spilled, find the volume of water in the tank that finally reached the society.
- From a tank, completely filled to its brim, water equal to $\frac{2}{5}$ of its capacity was taken out. 130 litres of water was added to the tank leaving it only $\frac{1}{6}$ empty. Find the capacity of the tank.
- Program to check if water tank overflows when n solid balls are dipped in the water tank in C++
- Find amount of water wasted after filling the tank in C++
- A cylindrical water tank of diameter $1.4\ m$ and height $2.1\ m$ is being fed by a pipe of diameter $3.5\ cm$ through which water flows at the rate of $2$ metre per second. In how much time the tank will be filled?
- A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his Held, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?

##### Kickstart Your Career

Get certified by completing the course

Get Started