One hose can fill a goldfish pond in 14 ​minutes, and two hoses can fill the same pond in 10 minutes. Find how long it takes the second hose alone to fill the pond.

Answer 1

(1/14) + (1/x) = 1/10

(x+14)/14x = 1/10

10x + 140 = 14x

x=35

This kind of problem is always difficult to explain and understand. The main point is that the times given are rates. For example, 1/14 is pond filled per minute. In this problem it should be obvious that the 2nd hose would take much longer alone since the one hose does the job almost as quickly as both together.