Answer:

[tex] \therefore [/tex] It will take 17.5 mins to fill the sink

Step-by-step explanation:

Let [tex] t [/tex] be the time it takes to fill the sink.

The pipe can fill 1/5 of the sink in a minute (since it takes 5 minutes to fill the sink). Similar to that, the drain may finish emptying 1/7 of the sink in a minute (since it takes 7 minutes to drain the full sink).

If the pipe and the drain are both open, so in one minute, the amount of the water going into the sink is:

• [tex] \rm{\frac{1}{5} - \frac{1}{7} = \frac{2}{35}} [/tex]

This means that in one minute, the sink is being filled with 2/35. Now, to fill the entire sink, we need to have 1 as the numerator (i.e, the sink needs to be filled completely). So we can set up the equation as:

• [tex] \rm{\frac{2}{35}t = 1} \\\\ \rm{t = \frac{35}{2} \approx \ 17.5} [/tex]

[tex] \therefore [/tex] It will take 17.5 mins to fill the sink