2 pumps can fill a water tank in 45 minutes when working together. Alone, the second pump takes 3 times longer than the first to fill the tank. How long does it take the first pump alone to fill the tank?

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rate = job/time

let the time of the faster pump be t min
let the time of slower pump be 3t min

rate of slower = job/(3t)
rate of faster = job/t
combined rate = job/(3t) + job/t
= (job + 3job)/(3t) = 4job/(3t)

time working together = job/(4job/3t)) = 45
job(3t)/(4job) = 45
3t/4= 45
t = 60

Using only the first pump would require 60 minutes.

Well, let's call the time it takes the first pump to fill the tank alone "x" minutes. That means the second pump takes 3x minutes to fill the tank alone since it takes 3 times longer.

If both pumps can fill the tank together in 45 minutes, that means their combined rate is 1/45 of the tank per minute.

Using the rate equation, the first pump can fill 1/x of the tank per minute, and the second pump can fill 1/(3x) of the tank per minute.

Since they are working together, their combined rate is 1/x + 1/(3x) = 1/45.

To solve for x, we'll need to find a common denominator. The common denominator is 3x.

So, (3 + 1)/3x = 1/45.

Simplifying, 4/3x = 1/45.

Now we can cross-multiply, which gives us 4 * 45 = 3x.

Simplifying further, 180 = 3x.

Finally, we divide both sides by 3 to solve for x, which gives us x = 180/3.

Therefore, the first pump alone takes 60 minutes to fill the tank.

Let's say the first pump can fill the tank in x minutes.

Since the second pump takes 3 times longer than the first pump, it would take the second pump 3x minutes to fill the tank.

Working together, the two pumps can fill the tank in 45 minutes, so their combined rate is 1/45 tanks per minute.

The rate of the first pump alone is 1/x tanks per minute.

The rate of the second pump alone is 1/(3x) tanks per minute.

Therefore, the combined rate of the two pumps is:

1/x + 1/(3x) = 1/45

To solve this equation, we need to find a common denominator:

(3 + 1)/(3x) = 1/45

4/(3x) = 1/45

Cross-multiplying:

4 * 45 = 1 * 3x

180 = 3x

Divide both sides of the equation by 3:

180/3 = x

60 = x

Therefore, it would take the first pump alone 60 minutes to fill the tank.

Let's start by assigning variables to the rates at which each pump fills the tank. Let's say the first pump fills the tank at a rate of "x" units per minute, and the second pump fills the tank at a rate of "y" units per minute.

Since the two pumps working together can fill the tank in 45 minutes, their combined rate is 1/45 of the tank filled per minute. Therefore, we can write the equation:

x + y = 1/45

According to the problem, the second pump takes three times longer than the first pump to fill the tank. This implies that the second pump has a rate of 1/3x units per minute. So our second equation is:

y = 1/3x

To solve these two equations simultaneously, we can substitute the value of y from the second equation into the first equation:

x + (1/3x) = 1/45

Multiply through by 45 to eliminate the fractions:

45x + 15 = 1

Subtract 15 from both sides:

45x = 1 - 15
45x = -14

Divide through by 45 to solve for x:

x = -14 / 45

So the first pump alone would take -14/45 units per minute to fill the tank. However, since time cannot be negative, we conclude that there may be an error in the given information or there is no solution for the first pump alone to fill the tank.