I was wondering if a teacher might take points off for giving the answer in hours and minutes. As a matter of accepted convention, if a question asks "how many hours", should the answer be _only_ in hours, or is it acceptable to give the answer in mixed units? It seems that the reason for this question asking how many hours is to prevent students from just answering 520 minutes, IOW, forcing them to make the conversion. If I was a math teacher I wouldn't take off for answering 8 hours and 40 minutes, but I've had some math teachers who probably would.
Thank you for the exercise. This actually looks to me like a physics problem, math is obviously involved. I never encountered unit checking until physics (not US). Yet at physics, this type of check did help me save some of my grades. Thanks 🤓
Greetings. It should take 8 hours and 42 minutes. From the details given, we will divide the number of gallons of water in the tank by the number of gallons drained in 1 minute to find the number of minutes taken to completely drain the tank. Thereafter, we will divide the number of minutes by 60 to determine the time taken in hours. That is 10, 400/20=520 minutes. Now, we will divide 520 by 60 to get 520/60=8.6666=8.7 rounded. That works out to 8 hours and 42 minutes.
I went the other way. I multiplied the rate of the pump by 60, to get 1,200 gallons per hour. 104,00/1,200=8.666666... If you didn't have a calculator, you can knock off the last 2 "0"s, and simplify to 104/12=8.66666666. The ultimate answer, is 8:40:00. (8 Hours, 40 minutes)
While I appreciate the power of algebra for complex non-intuitive problems, it is just not needed for this problem. It is trivial for any one with 5th grade math skils and a desire to figure it out. Gallons to move divided by pump speed, convert minutes to hours. then convert .666666 which is two thirds to minutes by multiplying by 60. I would give you and incomplete for not converting .6666666 hours to .39.999999 minutes and rounding the fraction of a second to 40 minutes or just knowing that 2/3s of an hour is 40 minutes. Im my rural school in the 70s, we had a class called Practical Math in 8th grade which required you to solve problems like this using basic math skills. Algebra, trig, etc are important if you are going on to a college degree that actually used calculus . But knowing how to figure this out with 6th grade math is much more important of the average person. Here's one I remember that you had to solve to be able to get out of eight grade. actual numbers are estimates of memory. Farmer Brown has a field to be fenced that was 300 by 400 hundred yards. He also needed a cross fence (narrow stretch) with a four foot gate and a main gate of 8 feet on one end. the fence would need four strands of barbed wire and a post every 8 feet. Wire comes in 100ft roles at a cost of $6.37 per roll. the 8 foot gate cost $ 47 and the 4 foot gate cost 2/3 of the larger gate. Fence posts cost $5.57 each. fence staples $4.48 per pound and equal about 42 per pound (you figure how many needed). Sales tax in the closest town hardware store is 5.2 % but driving another 40 miles to a busy ranch supply store out of the town the tax is only 3.2 percent What will all of this cost him at the local town? Extra credit: Will driving to the ranch store with his truck that gets 10 mpg ( gas $0.87 gallon) and take an extra two hours be a good idea (He values is time at about $6 per hour). Extra Extra credit: He estimates the job will take 6 days at 10 hours per day. He can hire two laborers $4.60 per hour each which will cut the time by 2/3s or more with him only contributing 2 hours per day as supervisor. Should he? Extra, Extra, Extra credit. After it was complete a neighbor asked to rent the pasture for a year. Said he would pay $136 per acre. What is his offer worth in $. (every farm boy knows the square footage in an acre or that it is a square just under 210 foot on a side). How long to fully pay for his investment. Final decision: With this knowledge in hand and making good use of his 8th grade education, He is ready to ask for and consider a bid from a contractor. Price would include all materials and labor. What would you pay. What if the contractor offered a monthly payment plan for 3 years at 6% compounded annually ? Tell me what you would do and why. Showing the work was about two pages of pencil work with a final summary and answers in Ink. No higher math skill needed but vital to the success of a farmer. Don't see much use for algebra here but tell me if you do.
Only one "existential" problem here. This can be solved in less than 30 seconds (make it one minute without a calculator). And as you asked us to do I will give you my reasoning. 60 minutes in an hour times 20 gallons = 1200 gallons drained per hour. 10400 gallons will then take 8,67 (I don't like too many "6" aligned ;) if you know what I mean) hours i.e. 10400/1200. So what's in it for me? Learning basic algebra. Fair enough.
I got 520 before, because I divided 20 by 10400 and then I went back and thought that was wrong because I needed to see how gallons there would be over 1 hour, so did 20 times 60 and then got that and divided that by 10400. So 1200/10400. I was typing this before the answer and now that I saw the answer I can't believe I got it right XD
I don't know how you could get the right answer by dividing in the wrong direction. If you divided "20 by 10400" you would have gotten 0.00192. If you divided "1200/10400" you would have gotten 0.115. If you're a student, dividing backwards is going to cause you _major_ problems. If you say, "Well, the way I think about it gets me the right answers", that won't cut it, since _everybody else in the world_ (including your teachers and textbooks) verbalizes and writes it in the opposite direction. Eventually, you will get so confused that you may _never_ be able to divide in the right direction! It's like how many ambidextrous people always have a problem figuring out which way to turn a screw.
"Your not going to encounter crazy word problems" Dude my teacher is an English-teacher-turned-math-teacher who writes like 2 paragraps per each word problem with a whole lot of useless garbage to throw us off.. it kills me 😭
I never understood having to write out some long word problem in order to get a fast basic number that can be easily calculated in a quick manner. I get showing your work, but in the real world life is all about proficiency. What is the most proficient way to do something. Am I wrong here?
Problems like this aren't about how easy they are to get an answer it's about having a foundation that allows you to know the fundamentals so that when you are dealing with a tough problem you know the basics to walk you through it .The more proficient you become the less there is a need to write things out in this manner. This helps you establish a good foundation that is all.
seems to me you would live your life writing out these things only because that is the way you were taught. The "foundation" becomes the way to do things, because you know no other way. @@davem45
10,400 gallons .. drained at a speed of 20 gallons a minute 10,400 / 20 = 520 minutes 60 minutes in an hour ..... 520/60 ..... 8 with 40 left over .. 8 hrs 40 minutes EDIT OK so I've watched your video and you say 8.66 hours I know the question said ''How many hours ?'' but who actually says 8.66 hours ?
I arrived in the air breathing community on October 23,1966. Because of my perception and reaction to life I avoided math, because I’m fairly healthy and believe math is the answer do you have a recommendation?
It’s nice to see all the detail.. but in real life work environments, I think an employer is not going to want that much time taken when there is a quick simpler approach as others have demonstrated.. core math curriculum is a waist.
He’s trying to pitch tutoring and materials sales to parents and students, so probably trying to project patience. I agree the explanations are too long (and in the weeds), so I skip those.
Again at minute 13:00 you don't explain WHY we divide both sides of the equation by 20. You give a lot of details along the way but when it comes to the most crucial operation you take it as granted that everyone knows what to do. It's not enough to say that "we apply basic algebra" at the end if your viewers don't already know this rule or its logic. If 20x = 10400 it means that we need to divide 10400 by 20 to find "X" but why? Because 20x means 20 times "X". Like if 4x = 20 we need to divide 20 by 4 to get "X". Like if we have 1 + x = 10 we need to substract 1 from 10 to get "X". Apart from that, nothing to say. But it's a big thing in my humble opinion.
