SOLUTION: To empty their swimming pool, the Johnsons decided to use the regular drain and pump. If it takes 15 hours for the pool to empty using the drain alone and 7 hours for the pool to e

Click here to see ALL problems on Rate-of-work-word-problems

Question 76431: To empty their swimming pool, the Johnsons decided to use the regular drain and pump. If it takes 15 hours for the pool to empty using the drain alone and 7 hours for the pool to empty using the pump alone, how long will it take for the pool to empty using both the drain and the pump?
? hours
(round to the nearest0.1)
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
If it takes 15 hours to empty the pool alone by using the drain, then one-fifteenth
of the pool is emptied each hour that the drain is open.
.
If it takes 7 hours for the pump alone to empty the pool, then one-seventh of the pool is
emptied each hour that the pump is on.
.
If the drain and the pump are both opened for t hours, then the pool is emptied and the
1 job of pool emptying is complete. In equation form this is:
.

.
Multiplying all these terms (both sides) by 15*7 eliminates the denominators and results in:
.

.
Add the two terms on the left side and multiply out the right side to get:
.

.
At this point you can solve for t by dividing both sides of the equation by 22 and this
results in:
.
hours
.
Rounding this to the nearest tenth of an hour says that the pump and drain will empty the
pool in 4.8 hours.
.
Hope this helps. The critical parts of the problem involve finding the individual rates
for the pump and the drain, recognizing that each of these rates times the common time that
the two methods of draining are operating together represents the combined amount of
drainage, and understanding that the combined amount of drainage is equal to 1 ... the
one job is completed.