the quantities s and t are positive This is a topic that many people are looking for. bluevelvetrestaurant.com is a channel providing useful information about learning, life, digital marketing and online courses …. it will help you have an overview and solid multi-faceted knowledge . Today, bluevelvetrestaurant.com would like to introduce to you Most US College Students Cannot Solve This Basic Math Problem. The Working Together Riddle. Following along are instructions in the video below:
“This is presh talwalkar alice and bob can complete a job in two hours. Alice alice and charlie can complete the same job in three hours. Bob and charlie can the same job in four hours. How long will the job take if alice bob and charlie work.
Together assume each person works at a constant rate. Whether working alone or working with others. This problem has been asked to students in us colleges to the professor s surprise. Many of the students set up the wrong equations and could not solve this problem can you figure it out give this problem.
A try and when you re ready keep watching the video for the solution before i get to the solution. Let me go over a common mistake in how students get to the wrong. Answer. They read the first sentence that alice and bob can complete a job in two hours and translate the names and the numbers into an equation.
They say this must mean that a b 2. They look at the second sentence that alice and charlie can complete the job in three hours and they similarly convert it to a c 3. The third condition that bob and charlie can complete the job in four hours gets converted to the equation b c. 4.
The question of how long it will take for all three of them working together gets translated into the question nof so to solve this system of equations they want to solve for a b c. So they can add up all the equations together we end up getting two terms of a two terms of b. And two terms of c to equal 2 3 4. If.
We group the factors summands we get n2a 2b 2c. 9..
We then divide by two and that gets us to a b c. 9. 2. 45.
Four. And a half . So evidently this will be the answer that many students get they would say that it takes 45. Hours for all three of them when working together.
But let s think about does this answer make any sense. We know that alice and bob take. Two hours alice and charlie take three hours and bob and charlie take four hours. But somehow when all three are working together they take four and a half hours.
This makes no sense. When three people work together it should take less time then when only two people work. Together but 45. Hours is more time.
So. This answer must be wrong not only were the equations set up incorrectly. But any student who submits this answer is not thinking about whether the answer makes any logical sense. So how do we solve this problem.
We need to set up the equations in the correct method. We know that alice and bob can complete a job in two hours..
So how do we translate this into an equation well if they complete the job in two hours that means the percentage of the job. That alice does in two hours plus the. Percentage of the job that bob does in two hours equals. 100 or that equals 1.
Now since they work at a constant rate. We can say the amount of the job. That alice does in two hours is 2 times the amount of the job that she does in one hour. And the same thing goes for bob so we now have a natural choice for our variables.
We can say the percentage of the job. That alice does in one hour will be the variable a and the percentage of the job. That bob does in one hour will be the variable b this leads to the equation that 2a 2b 1. And that s how we can translate this we can group this out to be 2 times 2x the quantity a b 1.
So we can now translate the second sentence. We have alice and charlie completing the job in three hours this will translate into 3 times. The quantity a c. 1.
Where c is the percentage of the job. That charlie completes in one hour. We also have that bob and charlie can complete the job in four hours so that would mean 4 times the quantity b c. 1.
Now we want to figure out what would happen if they all three work together. So we are needing to solve for the time t x..
A b c 1. We need to solve for this variable. So how do we do that well we can similarly add up all the equations. But we have different quantities of each of these variables.
So in order to get the same number of each variable. We re going to do a little trick. We re going to multiply each equation. So that there s a leading coefficient of 12.
Which is the lowest common multiple of 2 3. And 4. So the first equation will multiply by six this will get 12 times. The quantity a b to be equal to 6.
The second equation will multiply by four and the third equation will multiply by three we can now add up all of these equations we ll end up with 12a 2 times . 12b. 2 times . And.
12c 2. Times. . And this will be equal to 6 4.
3. We can factor out the 24 of each of these variables..
And that will be equal to 6 4 3. Which equals 13. We now divide by 13 and we end up with 24 divided by 13 times. The quantity a b c.
1. And that is what we wanted to figure out so we go back to our setup. And we can see that we get to the answer of 24 over 13. So the job will take 24 over 13 hours or about 1 hour.
And 51 minutes. And this is a sensible answer. Because it takes less time than any pair working together. Did you figure this out thanks for watching this video please subscribe to my channel.
I make videos on math you can catch me around around my blog mindyourdecisions that you can follow on facebook google. . And patreon you can catch me on social media. Preshtalwalkar and if you like this video.
Please check out my books. ” ..
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