Question 257730
The key to these kinds of problems is to figure out how much of the total task can be done by each person/entity <b>in one hour</b> and then use these figures to solve the problem.<br>
The pipe can do the entire task by itself in 12 hours. This means that the pipe can do 1/12 of the task in 1 hour.<br>
The hose can do the entire task by itself in 30 hours. This means that the hose can do 1/30 of the task in 1 hour.<br>
Working together the pipe and hose can do (1/12 + 1/30) of the task each hour.
{{{1/12 + 1/30 = 5/60 + 2/60 = 7/60}}}
Let x = the number of hours it takes both the pope and the hose to fill the pool. Then
{{{(7/60)x = 1}}}
Multiplying both sides by 60/7 we get:
{{{x = 60/7 = 8&4/7}}}