Pump

[johnjones]

I have no idea how to start or do this.

If pump A can empty the pool in 20 minutes, and pump B can empty in 30 minutes, how long should it take if both pumps are used?

Thanks.
I don't even know (was not given) values.. i.e. volume of pool and that stuff.

 

[Gene]

The secret is to figure what fraction is emptied in one minute. Just to illustrate, say one takes 6 minutes and the other takes 4 minutes. One pump empties 1/6 in one minute and the other empties 1/4 in one minute. Together they would empty 1/6 + 1/4 = 10/24 in one minute. So it would take both 24/10 = 2.4 minutes.
1/A+1/B=1/X
Study this and apply it to your problem.

 

[soroban]

Hello, johnjones!

Gene is absolutely correct . . . Here's another approach.

If pump A can empty the pool in 20 minutes, and pump B can empty in 30 minutes,
how long should it take if both pumps are used?

Let x = number of minutes for both pumps to empty the pool.

Pump A takes 20 minutes to empty the pool.
. . In one minute, it empties 1/20 of the pool.
. . In x minutes, it empties x/20 of the pool (some fraction of the pool).

Pump B takes 30 minutes to empty the pool.
. . In one minute, it empties 1/30 of the pool.
. . In x minutes, it empties x/30 of the pool (another fraction of the pool).

Together, in x minutes, they empty the entire pool ("1 pool").

. . . . . . . . . . . . . . . . . . . . x . . . x
There is our equation: . ---- + --- . = . 1
. . . . . . . . . . . . . . . . . . . 20 . . 30