math question?

Question

if a pump takes 18hrs to drain a pool, and another pump takes 12 hrs to drain a pool, how long will it take for both pumps to drain the pool

Answer 1

1/12+1/18=(3+2)/36in 1 hour both together will drain 5/36 tank
time taken by both to drain the tank=36/5=7hrs12 mts

Answer 2

let the 18hrs pump be pump A and the 12 hrs pump be pump B
In 1 hr, pump A will pump 1/18 of the volume of the pool while pump B will pump 1/12 of the pool's volume.

Together in 1 hr they'll pump 1/18+1/12
= (2+3)/36
=5/36

In total they'll take 36/5 hrs

ie 7hrs and 1/5hrs

=7hrs 12 Minutes

Answer 3

Its good to understand that the figures suggested to you

1/18 and 1/12

are rates. The first pump drains at the rate of one pool in 18 hours.

If a boat moves through the water at 6 miles/hour and is going down a stream that flows at 2 miles/hour, than you add the rates to see just how fast the boat is moving in relation to the shore.

Don't be confused because the pump rate is 1/18 - if the current downstream was 1/2 mile/hour, this rate would be stated as 1/2 (one mile in two hours).

So the scheme suggested to you

1/18 + 1/12 = 1/x

Is valid.

Answer 4

1/Pump A + 1/Pump B = 1 / Both Pumps

so, 1/18 + 1/12 = 3 + 2 / 36 = 5/36 = 1/7.2

so, 7 hours and 12 minutes

Answer 5

Let x be the gallons of water in the pool.
Let y be the gallons per hour that pump A pumps.
x = y * 18 since gallons = (gallons/hour)*hour
Let z be the gallons per hour that pump B pumps.
x = z * 12

Thus y*18=z*12
1.5y=z Meaning that pump B pumps 1.5 times as much per hour as pump A.

So we want to find how long it takes to pump x gallons when we are pumping at y + z gallons per hour.
y+z = y + 1.5y = 2.5y
So both pumps together pump 2.5 times as fast as y alone does.

y takes 18 hour to drain the pool, since we're pumping 2.5 times as fast we divide 18 by 2.5 and find it would take 7.2 hours to drain the pool utilizing both pumps.

Note that there are quicker ways to solve this problem but the way I solved it allows the maximum to be explained.

Answer 6

7.2 hours.

You take the pump that takes 18 hrs to drain as pump "A" and the pump that takes 12 hrs to drain as pump "B". Pump B is 1.5 times faster. So your total pumping capacity is A + 1.5*A=2.5*A.

In other words, your pump time is now 2.5 times faster than the case where you are using pump A alone.

So 18/2.5=7.2

Answer 7

pump a 1/18 hr^-1
pump b 1/12 hr^-1
combined 1/12+1/18=3/36+2/36=5/36 hr^-1
so it would take 36/5=7.2 hrs using both pumps.

Answer 8

Let

1/18 = Time it takes to fill the pool

1/12 = The time it takes to fill the pool

1 = The combined time it takes both to fill the pool

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1/18x + 1/12x = 1

36 (1/18x) + 36(1/12x) = 36(1)

36/18x + 36/12x = 36

2x + 3x = 36

5x = 36

5x/5 = 36/5

x = 7.2 hours

Insert the x value into the formula

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To find the minutes

Multiply 60 times 0.2

60 x 0.2 = 12 minutes

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The total time is 7 hours 12 minutes

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1/18x + 1/12x = 1

1/18(7.2) + 1/12(7.2) = 1

7.2/18 + 7.2/12 = 1

0.4 + 0.6 = 1

1 = 1

- - - - - - - - - s

Answer 9

ummm... 30?
Just kidding. The answer is 7 hours and 12 minutes

Answer 10

6 i think