Need a proportion and I will provide the following facts: One gallon equals 3785.41 milliliters. The sink can only hold 3 gallons of water. There was a total of 85 milliliters of water in 10 seconds. There was a total of 5 droplets of water in 10.14 seconds.
If a faucet leaks 85 milliliters in 10 seconds how many minutes will it take to fill the 3 gal sink?
- Posted:
- 3+ months ago by Anonymous...
- Topics:
- water, faucet, leak
Details:
Added 3+ months ago:
Also, what would the hours and seconds be?
Answers (2)
Get a ruler in your hands. Measure things until you start to understand how a ruler works. Measure some stuff and figure out where the center is. Say you measure a book and it's 7/8" thick. You look at your ruler and see that every eighth is divided into two sixteenths, so obviously half of 7/8" is going to be 7/16". If you write that out you have 1/2 x 7/8 = 7/16. And you notice that 1/2 is divided into 2/4 and then into 4/8 and so on, so you can convert anything to anything by multiplying all the numbers on top and then all the numbers on bottom.
Other rulers are divided into 10 and 100 parts. But an inch is still an inch, so anything on one ruler can be translated to the other ruler. A half inch on one ruler is 5/10 or 50/100 on the other. An eighth inch is just 12.5 marks when you have 100 marks per inch. A metric ruler divides an inch into 25.4 parts, so a half inch would be 12.7 of those parts. Pretty simple, isn't it? Practice this a bit and people will think you went to wizard school.
A conversion factor is a fraction equal to 1. You are given that one hour equals 60 minutes so you can write that as hr/60min=1 or 60min/hr=1 whichever works for you and drop it into an equation anywhere and it only changes the units.
ANSWER = You write this first so it looks like you know what you are doing. That gives you a bit of time to figure out what to do next.
ANSWER = 3gal x 3785.41ml/gal x 10sec/85ml x min/60sec
Ok, now we check everything. This is called sanity check and it is especially important in chemistry and physics where you might have a dozen or so conversions in a single equation. We have gal above the bar and again below, so that cancels. we have ml above and below, so that cancels. We have sec above and below, so that cancels. We have min above, and that appears in the answer like we want.
When you are sure everything is right, multiply all the numbers above the line and divide by all the numbers below.
ANSWER = 3gal x 3785.41ml/gal x 10sec/85ml x min/60sec = 22.267min
This word problem describes two quite distinct scenarios, which represent two fundamental concepts in our effort to understand the physical world, continuity and discreteness:
1. A continuous flow of water at 85 ml / 10 sec.
2. The water comes in discrete chunks (droplets d) of 5 d / 10.14 sec.
1st scenario:
85 ml / 10 sec = 8.5 ml / sec
1 gal = 3785.41 ml -> 3 gal = 11,356.23 ml.
how many minutes will it take to fill the 3 gal sink?
11,356.23 ml / (8.5 ml * sec^-1) = 1336.027059 sec. [There are 60 seconds / minute]
1336.027059 sec / (60 sec * min^-1) = 22.26711765 min.
That is 22 minutes plus 0.26711765 minutes. [1 min * 60 sec / min = 60 sec] Thus,
0.26711765 min * 60 sec / min = 16.027059 sec ≈ 16.03 sec.
And now we put it all together:
At a leak rate of 85 ml / 10 sec the 3 gallon sink will be full after
00 hrs : 22 min : 16.03 sec.
-----------------------------------------
2nd scenario:
1 d := 1 droplet
5 d / 10.14 sec = 0.493 d / sec.
But droplets do not come in fractions. How many ml are in one droplet?
(8.5 ml / sec) / (0.493 d / sec) = 17.24 ml / d.
How much time will it take to build up a droplet until it falls and adds to the contents of the sink?
(17.24 ml / d) / (8.5 ml / sec) = 2.028 sec / d.
How many droplets add up to 3 gal = 11,356.23 ml?
11,356.23 ml / (17.24 ml / d) = 658.714 d.
But, again, droplets do not come in fractions. After 658 droplets we'll have to wait another 2.028 sec. With the 659th droplet the sink will be filled, and
659 - 658.714 = 0.286 d = 4.93 ml will spill over.
In this scenario it will take
(2.028 sec / d) * 259 d = 1336.452 sec to fill the sink.
And
1336.452 sec = 22.2742 min =
00 hrs : 22 min : 16.452 sec.