Two sources of water filling tank

Question

suppose that we have two different sources of water. one is filling the tank full with 90 min and the other one is filling it up in 30 min. If we combined the two sources together, then how many minutes will take to fill the same tank ?

I found this question in a child book. I tries to solve it out and I found the most logical answer is 27,7 while 100/3=3.3 so 30-3.3=27.7

is this solution right ? others says it is 22,5 min. Can anyone relate?

Answer 1

Let us illustrate this information on a table: \begin{array}{| l | l | l | l |} \hline \textbf{Water Source} & \textbf{Time taken to fill} & \textbf{Amount of water filled} & \textbf{Rate of filling/minute} \\ \hline \text{Source 1} & 90 \text{ mins} & x & \frac{x}{90} \\ \hline \text{Source 2} & 30 \text{ mins} & x & \frac{x}{30} \\ \hline \text{Combined} & ? & x & \frac{x}{90}+\frac{x}{30} \\ \hline \end{array} The rate of filling per minute is taken by dividing the amount of water filled by the time taken to fill the tank.

Which is: $$\text{Rate}=\frac{\text{Amount}}{\text{Time}}$$ This can be rearranged to give the time taken to fill: $$\text{Time}=\frac{\text{Amount}}{\text{Rate}}$$ For the Combined sources, we just simply substitute these values: $$\text{Time}=\frac{x}{\left(\frac{x}{90}+\frac{x}{30}\right)}$$ $$\text{Time}=\frac{x}{\left(\frac{x}{90}+\frac{3x}{90}\right)}$$ $$\text{Time}=\frac{90x}{4x}$$ The $x$'s cancel, and give: $$\boxed{\text{Time}=22.5 \text{ mins}}$$

Answer 2

The part filled by tap $A $ in one minute $=\frac{1}{90} $.

The part filled by tap $B $ in one minute $=\frac {1}{30}$.

The part filled by taps $(A+B) $ in one minute $=(\frac {1}{90}+\frac {1}{30}) =\frac {4}{90} = \frac {1}{22.5} $.

Thus both pipes can fill in $22.5$ minutes. Hope it helps.

Answer 3

OK, so in the comments you explain your reasoning as:

So in 90 min the tank will be filled by source B. thats means in the first 30 min of source B will be filling the tank 1/3 of the whole amount of the 100% tank right ? that's why I divided 100 over 3 to get the percentage of filling in the first 30 min of 90 min. After that, I subtract the 3,3 from the fast 30 min filling of source A

Where is your reasoning mistake?

OK, first your basic arithmetic is a bit off: 100 over 3 is 33.3, not 3.3. That is, if we use source B alone, then the percentage of the tank that would be filled after 30 minutes is 33.3%, not 3.3%. So, you are right that it is 1/3, but 1/3 of 100% is 33.3%.

OK, but now you make a second, and much more serious mistake: you subtract this percentage from the time (30 minutes) it takes for source A to fill the tank. But notice how these are completely different kinds of quantities! And you cannot use basic arithmetic when you are talking about different kinds of units or measurements. For example, you might just as well have subtracted 1/3 from 30 .. and that would equally have been a mistake: you are comparing apples and oranges!

Hope that helps!