Basic Math Word Problem (Proportions): Get Better in Algebra

TabletClass Math:


Math Notes:

[percenthealth]

I got it by 20X60 = 1200 then dividing 10400 by 1200 which is 8.6 hours.

[virgilviereckjr.]

Thank you.
It’s been a long time since I’ve done any math. Common knowledge kind of slips away.

[shidamirzaie]

thank you teacher
you are the best teacher
and first teacher I understand what he says ❤🎉

[stevenjohnson]

8 hour forty minutes. multiply 20 gallons per minute by 60 which is 1200 gallons per hour divide 10400 by 1200 and 8 hour 40 minutes is the answer

[danieldennis]

20g/m; 60m=h; 1200g/h=10400x= 8.6repeating or 8 hours 40 minutes

[devonwilson]

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.

[vincentrobinette]

I went the other way. I multiplied the rate of the pump by 60, to get 1, 200 gallons per hour. If you didn't have a calculator, you can knock off the last 2 "0"s, and simplify to The ultimate answer, is 8:40:00. (8 Hours, 40 minutes)

[calvinmasters]

Invert.
20 gal/min = 1/20 min/gal.
Total minutes = (1/20) * 10, 400

[aryusure]

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.

[Herlongian]

104/12 hours. There is no instruction to convert to mixed number. Or reduce. So could just leave it at 10400/1200 hours.

[Astrobrant]

Why 8.66? Shouldn't it be 8.67? (Or 8 ⅔)

[Rational_thinker_]

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 which is two thirds to minutes by multiplying by 60.

I would give you and incomplete for not converting hours to 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.

[edsherrod]

I love word problems you can set up as a proportion 🙂

[mr.mxyzptlks]

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 🤓

[chikeokoye]

10400/20mins=520mins

520/60=8.67hrs

[rotteson]

I would suggest in real world application to convert 8.67 Hrs to 8Hrs 40 Mins, because not everyone knows 0.67 is approximately 40Mins

[clydebennish]

8.7 hours. 20 gal per min... 1200 gal per hour... 10400/1200 = 8.7 or 8:42
Slide rule did it again.

[dnarna]

Where is the pump, man??? I need to see some specs first!!

[waberoid]

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

[s.j.r]

10400 gal ÷ ( 20 gal/m × 60 m/h )
10400 gal ÷ 1200 gal/h
8hour 40min