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# If Two Pipes Function Simultaneously, a Reservoir Will Be Filled in 12 Hours. One Pipe Fills the Reservoir 10 Hours Faster than the Other. How Many Hours Will the Second Pipe Take to Fill the Reservoir? - Mathematics

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#### Question

If two pipes function simultaneously, a reservoir will be filled in 12 hours. One pipe fills the reservoir 10 hours faster than the other. How many hours will the second pipe take to fill the reservoir?

#### Solution

Let the first pipe takes x hours to fill the reservoir. Then the second pipe will takes (x + 10) hours to fill the reservoir.

Since, the faster pipe takes x hours to fill the reservoir.

Therefore, portion of the reservoir filled by the faster pipe in one hour = 1/x

So, portion of the reservoir filled by the faster pipe in 12 hours = 12/x

Similarly,

Portion of the reservoir filled by the slower pipe in 12 hours =12/(x + 10)

It is given that the reservoir is filled in 12 hours.

So,

12/x+12/(x+10)=1

(12(x+10)+12x)/(x(x+10))=1

12x + 120 + 12x = x2 + 10x

x2 + 10x - 24x - 120 = 0

x2 - 14x - 120 = 0

x2 - 20x + 6x - 120 = 0

x(x - 20) + 6(x - 20) = 0

(x - 20)(x + 6) = 0

x - 20 = 0

x = 20

Or

x + 6 = 0

x = -6

But, x cannot be negative.

Therefore, when x = 20then

x + 10 = 20 + 10 = 30
Hence, the second pipe will takes 30hours to fill the reservoir.

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