Not my homework, just practice. I'm translating this:
Two pumps fill a pool in 3 hours. One pump alone would fill it in 4 hours and 20 minutes. In what time would the second pump fill the pool (alone)?
Or:
Two combines work a field in 3 hours and 15 minutes. One alone would do the job in 7 hours. What time would it take the second one?
You can do both or just one.
Please explain your work. My thinking cap is not on tonight.
Two pumps fill a pool in 3 hours. One pump alone would fill it in 4 hours and 20 minutes. In what time would the second pump fill the pool (alone)?
Or:
Two combines work a field in 3 hours and 15 minutes. One alone would do the job in 7 hours. What time would it take the second one?
You can do both or just one.
Please explain your work. My thinking cap is not on tonight.
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Here's how I set it up and logic it out:
So, let's start with a pool of volume V.
It takes Pump 1, that pumps at a rate of R1, 4 hours and 20 minutes (4.33 hours) to fill up a pool of volume V.
Since Rate = Volume/Time, we can rearrange and get Volume = Rate*Time.
Therefore, we can say:
V = R1 * 4.33 hr
Applying that same logic to the fact that it takes both pump 1 (R1) and pump 2 (R2) 3 hours to fill that same pool together, we get:
V = 3 * R1 + 3 * R2
Now, we can substitute 'V' in the second equation for what we showed V equals in the first equation (4.33*R1). Getting:
4.33*R1 = 3*R1 + 3* R2
Moving our variables around shows the following:
1.33*R1 = 3*R2
R1 = 3*R2/1.33 = 2.25*R2
R1 = 2.25*R2
Going back to our first equation, V = R1 * 4.33 hr, we can plug in 2.25*R2 in the place of R1, getting
V = R1 * 4.33 hr = (2.25*R2) * 4.33 hr = 9.75 * R2
Now, we can solve for V / R2 which would be Volume / Rate to give us time, or just know that the 9.75 multiplying the rate R2 must be the time required.
So, the time for Pump 2 to fill the pool is 9.75 hours or 9 hours and 45 minutes.
So, let's start with a pool of volume V.
It takes Pump 1, that pumps at a rate of R1, 4 hours and 20 minutes (4.33 hours) to fill up a pool of volume V.
Since Rate = Volume/Time, we can rearrange and get Volume = Rate*Time.
Therefore, we can say:
V = R1 * 4.33 hr
Applying that same logic to the fact that it takes both pump 1 (R1) and pump 2 (R2) 3 hours to fill that same pool together, we get:
V = 3 * R1 + 3 * R2
Now, we can substitute 'V' in the second equation for what we showed V equals in the first equation (4.33*R1). Getting:
4.33*R1 = 3*R1 + 3* R2
Moving our variables around shows the following:
1.33*R1 = 3*R2
R1 = 3*R2/1.33 = 2.25*R2
R1 = 2.25*R2
Going back to our first equation, V = R1 * 4.33 hr, we can plug in 2.25*R2 in the place of R1, getting
V = R1 * 4.33 hr = (2.25*R2) * 4.33 hr = 9.75 * R2
Now, we can solve for V / R2 which would be Volume / Rate to give us time, or just know that the 9.75 multiplying the rate R2 must be the time required.
So, the time for Pump 2 to fill the pool is 9.75 hours or 9 hours and 45 minutes.
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1. So, if it's only one pump opened, it will go like this:
3 * (1/4.2 + 1/x) = 1 (because they are filling one pool)
3 * (x+ 4.2/4.2x) = 1
3x + 12.6/4.2x = 1 (we're getting rid of a fraction by multiplying it with 4.2) / x4.2
3x + 12.6 = 4.2 (now we deal with 3) / : 3
x + 4.2 = 1.4x
4.2 = 1.4x - x
x = 4.2 / 0.4
x = 10.5 hours
Hope you got it :-)
3 * (1/4.2 + 1/x) = 1 (because they are filling one pool)
3 * (x+ 4.2/4.2x) = 1
3x + 12.6/4.2x = 1 (we're getting rid of a fraction by multiplying it with 4.2) / x4.2
3x + 12.6 = 4.2 (now we deal with 3) / : 3
x + 4.2 = 1.4x
4.2 = 1.4x - x
x = 4.2 / 0.4
x = 10.5 hours
Hope you got it :-)