word problem

Question

one pump can drain a pool in 12 minutes. When the second pump is also uses, the pool only takes 3 minutes to drain. How long would it take the second pump to drain the pool if it were the only pump in use

Answer 1

Steve & Jim are correct, but perhaps this can help you think about the relationship between the pumps & water:

 

If the first pump takes 12 minutes alone, and both pumps together do it in 3 minutes, then we know that the first pump empties 1/4 of the pool in the time it takes the second pump to empty 3/4 of the pool. Emptying 3/4 of a pool in 3 minutes is the same as 1/4 of the pool each minute. Therefore, the second pump does the job in 4 minutes.

Answer 2

Rates:

 

Pump 1: r1 = 1 pool/12 minutes

 

Pump 2: r2 = ?

 

1 pool = r1*3 + r2*3

 

r1 + r2 = 1/3

 

r2 = 1/3 - r1 = 1/3 - 1/12

 

r2 = 4/12 - 1/12 = 3/12

 

r2 = 1 pool/4 minutes

 

By itself, the second pool could drain the pool in 4 minutes.

Answer 3

Patricia,

            Let V=volume of the pool. Using the general rate and time equation V=R*T and applying it the the first instance gives

                        V=R₁*12 so R₁=V/12.  now let R₂=pumping rate of the second pump so V=(R₁+R₂)*3 so R₁+R₂=V/3 we know what R₁ is so R₂=V/3 -V/12=3V/12 or V/4. If we now use this pump to empty the pool it will take V/R₂ minutes  or T=V/(3V/12) or 4 minutes to empty.

 

Hope this helps

Jim