tab B alone takes 2 minutes longer than tap A to fill one tub. Working together, they can fill the tub 4 times in 5 minutes. How long does it take tap A (alone) to fill one tub? ((to 2 decimal places if necessary))

2. Let a = tap A time.

Then tap b is A+2

They fill the tub 4 times in 5 minutes.

$\frac{1}{a}+\frac{1}{a+2}=\frac{4}{5}$

Solve for a and b will be two minutes more.

3. could you define all the variables and where the numbers and equations come from... i just want to really understand the problem

like for example why is it 1/a? etc

4. Originally Posted by finch41
could you define all the variables and where the numbers and equations come from... i just want to really understand the problem

like for example why is it 1/a? etc
Hi, finch41. As galactus explained, $a$ is the amount of time it takes tap A to fill 1 tub. That means tap A fills 1 tub per $a$ minutes, so the rate is $\frac1a\text{ tubs/min}$. Similarly, tap B takes $a + 2$ minutes (2 minutes more than tap A) to fill the tub, so it has a fill rate of 1 tub per $a + 2$ minutes, or $\frac1{a + 2}\text{ tubs/min}$. But, when both taps are on, they fill 4 tubs every 5 minutes, so we have a rate of $\frac45\text{ tubs/min}$. This gives us the equation,

$\text{rate of tap A}\;+\;\text{rate of tap B}\;=\;\text{combined rate}\Rightarrow\frac1a + \frac1{a + 2} = \frac45$

Solve for $a$.