A hose can fill a swimming pool in 6 hours.

Question

other hose needs 3 more hours to fill the pool than the two hoses combined. How long to fill it with both

Answer 1

Hose A fills pool in 6 hours.  1/6 pool per hour

Hose B fills pool in x hours.  1/x pool per hour.

together they fill 1/x + 1/6 pools per hour.

together it takes 1/(1/x+1/6) hours per pool using both hoses.

This time is 3 hours faster than hose B.

1/(1/x+1/6)=x-3

6x/(x+6)=x-3

6x=x²+3x-18

x²-3x-18=0

(x-6)(x+3)=0 x=6 is only possible answer.

time for both hoses is 1/(1/6+1/6)=3 hours

1/(1/6+1/6)=6-3  3=3

 

Answer 2

lets suppose that when the two hoses fill the pool together, it takes 2 hours.

Then how much of the pool gets filled by the hose that takes 6 hours to fill the pool by itself.

Well, if it fills for only 2 hours, but would require 6 hours, then it fills 2/6 = 1/3 of the pool.

 

So we got this fraction by dividing the time for the hoses working together by the time working alone.

 

Similarly, if it takes x hours filling together, the 6 hour hose will fill x/6.

 

The other hose filling alone would take x+3 hours filling alone

 

So this hose will fill x/(x+3)

 

Together the fractions must add up to 1

 

x/6 + x/(x+3) = 1

 

multiply everything by 6(x+3)

 

x(x+3) + 6x = 6(x+3)

 

x² + 3x + 6x = 6x + 18

 

x² +3x - 18 = 0

 

(x+6)(x-3) = 0

 

x = -6   negative hours is not possible so we ignore this answer

 

x = 3 hours with hoses combined

 

Check\

 

3/6 + 3/6 = 1 

1=1