Question

HELP!I'm really bad at word problems.
:This is about rate problems:

Four years ago, the water in the apartment complex pool was emptied using a single pump. That took 33 hours. To get the job done more quickly this year, the apartment manager is going to use an additional pump that would take 22 hours to empty the entire pool on its own. If the pool contains 99,000 gallons of water, how much faster will the pool empty using both pumps at the same time than it did four years ago?

To the nearest tenth of an hour, the pool will be emptied _____ hours faster.

Answer 1

these use rate * time = amount

we need to figure out the rates.
pool contains 99,000 gallons
single pump. That took 33 hours

that means the rate for this pump is 99000 gals/33 hours
which can be simplified to 3000 gal/hr (3000 gallons per hour)

any idea what the rate of the second pump is ?

Answer 2

um 99000/22?

Answer 3

yes, and you should keep the units i.e. gals/hour
and of course, simplify it

Answer 4

Okay so its 4500 gals/ per hour ?

Answer 5

yes.

these pumps can operate in parallel (at the same time) so what is the combined rate of gals/ hour when both are working together ?

Answer 6

so its 3000gals+4500gals

Answer 7

which is 7500 gal/hour

now use rate * time = 99,000 gals

Answer 8

you know the rate, you know the amount of water you have to pump. You can solve for time

Answer 9

so 99000/7500= 13.2

Answer 10

Okay thanks! before you go can you help me with another question?

Answer 11

make that
\[ \frac{ 99000\ gal}{7500 \frac{ gal}{hour} }= 13.2 \ hours \]