Pool

If water flows into the pool by two inlets, fill the whole for 19 hours. The first inlet filled pool 5 hour longer than the second. How long pool take to fill with two inlets separately?

Correct answer:

t₁ =  40.66 h
t₂ =  35.66 h

Step-by-step explanation:

$$\begin{gathered} {\displaystyle \frac{1}{t_1}}+{\displaystyle \frac{1}{t_2}}={\displaystyle \frac{1}{19}} \\ {t}_2=t_1-5 \\ 1\mathrm{/}{t}_1+1\mathrm{/}(t_1-5)=1\mathrm{/}19 \\ 19\ast (x-5)+19\ast x=(x-5)\ast x \\ 19\cdot (x-5)+19\cdot x=(x-5)\cdot x \\ -x^2+43x-95=0 \\ {x}^2-43x+95=0 \\ a=1;b=-43;c=95 \\ D=b^2-4ac=43^2-4\cdot 1\cdot 95=1469 \\ D>0 \\ {x}_{1,2}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{43\pm \sqrt{1469}}{2}} \\ {x}_{1,2}=21.5\pm 19.163767896737 \\ {x}_1=40.663767896737 \\ {x}_2=2.3362321032632 \\ \text{ Factored form of the equation: } \\ (x-40.663767896737)(x-2.3362321032632)=0 \\ {t}_1>0 \\ {t}_1=x_1=40.6638=40.66\text{ h} \end{gathered}$$

Our quadratic equation calculator calculates it.

$$\begin{gathered} t_2>0 \\ {t}_2=t_1-5=40.6638-5=35.66\text{ h} \end{gathered}$$

Try another example

Showing 3 comments:

Math student

1/t1+1/(t1-10)=1/18
multiply each term by18(t1)(t1-10)
that results in
18(t1-10)+18t1=t1(t1)(t1)-10t1
using the quadratic formula results in t1=-49.6 and 3.63
ubless i made a mistake, your calculations need reexamination!!!        Correct me, please.

2 years ago  2 Likes Like

Dr Math

right side of equation is wrong - should be t1*(t1-10) = t1² - 10*t1 now t1³-10t1

2 years ago  Like

Math student

the problems seems to have changed - - - t2 is now equal t1-6

therefore 1/t1+1/(t1-6)=1/18
multiplying each term by18(t1)(t1-6) ==== 18(t1-6)+18t1=t1(t1-6), simplifying further 18t1-108+18t1=t1²-6t1
or 0=t1²-6t1-18t1+108
graphing y=18(t1-6)+18t1-t1(t1-6) results in t1=39.25 hours and t2=39.25-6=33.25 hours (same as your NEW answer!!!!

2 years ago  Like

Related math problems and questions:

• Two pipes
  How long will the pool be filled with a double supply pipe if it takes the pool to fill the first pipe by 4 hours longer and the second pipe 9 hours longer than both pipes open at the same time?
• Water pool
  Pool with volume 990hl completely filled, if water flows by one tap 8 hours and by second tap 6 hours. First tap give 10hl more than second per hour. How many hl flows in each of them in an hour?
• Water reservoir
  The water reservoir is filled through one inlet 4 hours later than both together, then another inlet 9 hours later. For how long is filled by each separately?
• Tributaries
  The first tributary fill pool with water in 15 hours. The second tributary fill pool in 10 hours. For how many hours the pool is filled with both tributaries?
• Four pavers
  Four pavers would pave the square in 18 days. How many pavers do you need to add to done work in 12 days?
• Three pumps
  We are filling the pool. The first pump would be filled in 12 hours, the second pump in 15 hours. If all three pumps were running at the same time, it would fill the pool for 4 hours. How long would the pool fill only with the third pump?
• The dam
  The water reservoir is filled with first tributary for 25 hours second tributary for 35 hours. Some time were both inlets open, then a second tributary closed and the tank was filled in four hours. What time water flowed from both tributaries? (Expressed
• The pool
  The pool contains 220 m³ of water. The pool can be emptied either: a) 10 hours of pipe B and 8 hours of pipe A, or b) 10 hours of pipe A and 7 hours of pipe B. How many cubic meters of water will flow in 1 hour from pipe A and how many from pipe B?
• Tank No 8
  Tank is filled by one inlet valve with a flow rate of 12 liters per second in 72 minutes. How long take the tank to fill, if we open half an hour after one more inlet?
• Pool
  Pool is filled with two water supply. The first supply fill pool for nine hours, the second for six hours. How many hours will take fill the pool when the water flows in through the first supply 3 hours and then we will open a second supply?
• 4 pipes
  The tank flows out by 4 pipes in 6 hours 120 hl water. How much water flows out of 5 pipes of the same diameter in 14 hours?
• Speed of Slovakian trains
  Rudolf decided to take the train from the station 'Ostratice' to 'Horné Ozorovce'. In the train timetables found train Os 5409 : km 0 Chynorany 15:17 5 Ostratice 15:23 15:23 8 Rybany 15:27 15:27 10 Dolné Naštice 15:31 15:31 14 Bánovce nad Bebravou 15:35 1
• Tributaries
  We can fill the pool with two different tributaries. The first inflow would fill the pool in 18 hours, both in 6 hours. How many hours would the pool fill with a second inflow?
• Two pipes
  One pipe fill one-fifth volume 20 minutes before by second one. The two pipes together will fill the tank in two hours. How long is will fill tank each pipe separately?
• Pumps 3
  Two pumps of the same power fill the garden pool for 10 hours. How many of these pumps would have to use if we want to shorten the filling of the pool to four hours?
• Pool 2
  The first supply by the pool fill for five hours and the second fill for six hours, drain should be drained for 15 hours. For how many hours the pool is full, when we open both inlet now and outlet open two hours later?
• Oil tank and pipes
  The underground oil tank can be filled by two oil pipelines. The first is filled in 72 hours and the second in 48 hours. How many hours from the moment when first pipeline began to fill the oil is it necessary to start filling it with the second to fill i