cherrie3sg
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One tap fills a tank in 5 mins and the 2nd tap fills the same tank in 3 mins. how long does it take to fill the tank if both taps are on? 
thinking skill
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Hello, cherrie3sg!
\(\displaystyle \text{The first tap takes 5 minutes to fill the tank.}\)
. . \(\displaystyle \text{In one minute, it can fill }\tfrac{1}{5}\text{ of the tank.}\)
\(\displaystyle \text{The second tap takes 3 minutes to fill the tank.}\)
. . \(\displaystyle \text{In one minute, it can fill } \tfrac{1}{3}\text{ of the tank.}\)
\(\displaystyle \text{Together, in one minute, they can fill }\tfrac{1}{5} + \tfrac{1}{3} \:=\:\tfrac{8}{15}\text{ of the tank.}\)
\(\displaystyle \text{Therefore, together they can fill the tank in }\frac{1}{\frac{8}{15}} \:=\:\tfrac{15}{8} \:=\:1\tfrac{7}{8}\text{ minutes.}\)
\(\displaystyle \text{The first tap takes 5 minutes to fill the tank.}\)
. . \(\displaystyle \text{In one minute, it can fill }\tfrac{1}{5}\text{ of the tank.}\)
\(\displaystyle \text{The second tap takes 3 minutes to fill the tank.}\)
. . \(\displaystyle \text{In one minute, it can fill } \tfrac{1}{3}\text{ of the tank.}\)
\(\displaystyle \text{Together, in one minute, they can fill }\tfrac{1}{5} + \tfrac{1}{3} \:=\:\tfrac{8}{15}\text{ of the tank.}\)
\(\displaystyle \text{Therefore, together they can fill the tank in }\frac{1}{\frac{8}{15}} \:=\:\tfrac{15}{8} \:=\:1\tfrac{7}{8}\text{ minutes.}\)
BigGlenntheHeavy
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\(\displaystyle cheerie3sg, \ another \ way \ to \ look \ at \ it.\)
\(\displaystyle One's \ rate \ multiply \ by \ the \ time \ it \ takes \ one \ to \ complete \ the \ job \ = \ unity(1).\)
\(\displaystyle Hence, \ Rate \ X \ Time \ = \ Fraction \ of \ Work \ Done.\)
\(\displaystyle In \ other \ words, \ if \ one's \ rate \ is \ 1/5, \ then \ it \ would \ take \ 5 \ minutes \ to \ complete \ the \ job\)
\(\displaystyle 1/5 \ X \ 5 \ = \ 5/5 \ =1 \ unity, \ job \ is \ completed.\)
\(\displaystyle Now, \ two \ taps \ working \ in \ unison \ with \ different \ rates \ will \ complete \ the \ job \ by \ the \ lesser \ of\)
\(\displaystyle their \ respective \ time, \ (common \ sense)\)
\(\displaystyle Ergo, \ rate \ of \ first \ tap \ X \ time(t) \ = \ fraction \ of \ its \ work \ done, \ = \ t/5\)
\(\displaystyle and \ rate \ of \ second \ tap \ X \ time(t) \ = \ fraction \ of \ its \ work \ done, \ = \ t/3\)
\(\displaystyle Therefore, \ the \ fraction \ of \ work \ done \ by \ the \ first \ tap \ combined \ with \ the \ fraction\)
\(\displaystyle of \ work \ done \ by \ the \ second \ tap \ must \ equal \ the \ whole \ piece \ of \ work, \ or \ 1;\)
\(\displaystyle hence, \ solution: \ t/5+t/3 \ = \ 1 \ \implies \ t \ = \ 15/8 \ minutes, \ the \ time \ it \ takes \ when \ they\)
\(\displaystyle are \ both \ working \ together.\)
\(\displaystyle One's \ rate \ multiply \ by \ the \ time \ it \ takes \ one \ to \ complete \ the \ job \ = \ unity(1).\)
\(\displaystyle Hence, \ Rate \ X \ Time \ = \ Fraction \ of \ Work \ Done.\)
\(\displaystyle In \ other \ words, \ if \ one's \ rate \ is \ 1/5, \ then \ it \ would \ take \ 5 \ minutes \ to \ complete \ the \ job\)
\(\displaystyle 1/5 \ X \ 5 \ = \ 5/5 \ =1 \ unity, \ job \ is \ completed.\)
\(\displaystyle Now, \ two \ taps \ working \ in \ unison \ with \ different \ rates \ will \ complete \ the \ job \ by \ the \ lesser \ of\)
\(\displaystyle their \ respective \ time, \ (common \ sense)\)
\(\displaystyle Ergo, \ rate \ of \ first \ tap \ X \ time(t) \ = \ fraction \ of \ its \ work \ done, \ = \ t/5\)
\(\displaystyle and \ rate \ of \ second \ tap \ X \ time(t) \ = \ fraction \ of \ its \ work \ done, \ = \ t/3\)
\(\displaystyle Therefore, \ the \ fraction \ of \ work \ done \ by \ the \ first \ tap \ combined \ with \ the \ fraction\)
\(\displaystyle of \ work \ done \ by \ the \ second \ tap \ must \ equal \ the \ whole \ piece \ of \ work, \ or \ 1;\)
\(\displaystyle hence, \ solution: \ t/5+t/3 \ = \ 1 \ \implies \ t \ = \ 15/8 \ minutes, \ the \ time \ it \ takes \ when \ they\)
\(\displaystyle are \ both \ working \ together.\)
cherrie3sg said:One tap fills a tank in 5 mins and the 2nd tap fills the same tank in 3 mins. how long does it take to fill the tank if both taps are on?
If the taps were filling seperate tanks concurrently,
then after 3 minutes, one tank would be full and the other will be full to \(\displaystyle \frac{3}{5}\)ths capacity.
That's \(\displaystyle \frac{8}{5}\) tanks filled.
\(\displaystyle 3\left(\frac{5}{8}\right)\ mins....\frac{8}{5}\left(\frac{5}{8}\right)\ tanks\ =\ 1\ tank.\)