If it takes a big pump 3 hours to drain a pool and 12 hours with a small pump. How long will it take to drain a pool with both

Question

 3 hours to drain pool with a big pump. Same pool takes 12 hours to drain pool.  How long to drain the pool with both pumps. 

Answer 1

I kind of hate these problems because teachers expect you to use an equation when it is completely unnecessary.

pump 1 can do 1/3 of the job in 1 hour.

pump 2 can 20 1/12 of the job in an hour.

 

Together they can do 1/3+1/12 = 5/12 of the job in 1 hour.

 

So 5/12 H = 1 job

so H=12/5 or 2.4 hours.

 

Hope this helops.

Answer 2

lets call the 3 hours 3x and the 12hours 12y since these arena is scalable we can assume randomly that the pool is say 36 big.

 

We learn that 3x drained the pool at a rate of 12 per unit and 12y drained the pool at a rate of 3 per unit. The new rate is the sum, which is 15. it takes 36/15 hours