Question 1189793
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Here is another solution method using reasoning and simple arithmetic only -- like the method shown by tutor @ikleyn but with slightly different calculations.<br>
The smaller hose takes 4 times as long as the larger to fill the pool, so when the two work together the larger hose does 4/5 of the work and the smaller hose does 1/5.<br>
The two together fill the pool in 20 minutes; so the smaller hose does 1/5 of the work in 20 minutes.  That means it takes the smaller hose 20*5=100 minutes to fill the pool by itself.<br>
ANSWER: 100 minutes<br>