Awater tank can be filled in 10 hours by an inlet pipe and empited in 14 hours by an outlet pipe. how long will it take to fill the tank if both pipes are left open?

t = amount of hours it takes to fill the tank.

let's say it takes "t" hours to do the whole tank, and we know the inlet pipe can do the whole tank in 10 hours, so, how much has it done in 1 hour only? well, since it takes 10 hours to do the whole tank, in 1 hour the inlet pipe has only done 1/10 of the whole job.

likewise, the outlet pipe can empty the whole thing in 14 hours, so how much has it emptied in 1 hour alone? well 1/14 of the whole tank.

keeping in mind both have done in 1 hour, only 1/t of the whole thing.

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).