A paint-mixing machine has 2 inlet pipes. One takes 1 hour less than the other to fill the tank. Together they fill the tank in 3 hours. How long would it take each of them alone to fill the tank?
Thank you!!!
time=1/(1/timefast + 1/(timefast+1)
3(1/timefast + 1/(timefast+1))=1
solve for timefast. For the other unit, add one hour.
multiply tf(tf+1) to each side to get started.
To solve this problem, let's assume that the slower pipe takes x hours to fill the tank. Then, the faster pipe will take x - 1 hours to fill the tank.
To find the rate at which each pipe fills the tank, we can calculate the fraction of the tank filled per hour.
We know that in 1 hour, the slower pipe fills 1/x of the tank, and the faster pipe fills 1/(x-1) of the tank.
Now, let's calculate the combined rate of the two pipes when they work together. In 1 hour, they fill one-third (1/3) of the tank, since it takes them 3 hours to fill the entire tank.
Setting up an equation, we have:
1/x + 1/(x-1) = 1/3
To solve this equation, we can find a common denominator and simplify:
[(x-1) + x]/[x(x-1)] = 1/3
Simplifying further:
(2x - 1)/(x^2 - x) = 1/3
Now, let's cross-multiply to eliminate the fractions:
3(2x - 1) = x^2 - x
Simplifying further:
6x - 3 = x^2 - x
Setting this equation to zero, we have:
x^2 - 7x + 3 = 0
Using the quadratic formula, we find that x ≈ 6.55 or x ≈ 0.457.
However, since the slower pipe always takes more time to fill the tank than the faster pipe, the value of x cannot be less than 1. Therefore, x ≈ 6.55 is not a valid solution.
Therefore, the slower pipe takes approximately 6.55 hours to fill the tank, while the faster pipe takes approximately 5.55 hours to fill the tank.