Supposedly basic Minimal Info Math Problem for Junior HS : Analyse

V=D/T

Therefore D=VT

So you have D= 10R for the distance traveled running

D= 5(Total Time - R) for the distance traveled walking

Therefore D= 10R + 5(Total Time - R)

If you factor that out, D= 10R + 5total time - 5R

So D= 5R + 5total time

Isolate total time, (D-5R)/5 = Total Time

Pretty sure that is all you can do

It took me like 6 minutes.

A 12 year old could solve it in about the same time or even less, because they don't have to explain it.

It took me about 30 seconds.

Total Time = T

Time Running = R

Total distance:

D = 10*R + 5*(T - R)

Dirtengineer wrote:It took me about 30 seconds

i doubt it...

3 minutes, but I have a PhD in physics.

Same as first responder

Run @ 10 km/h, Walk @ 5 km/h

let R = time running, let W = time walking

D = 10R + 5W

T = R + W = ? (Given R)

5W = D - 10R

W = D/5 - 2R

therefore T = R + W = D/5 - R

I don't know if I would have been capable of solving this at that age. I don't think I would have been comfortable with leaving R (and D) in the solution.

Having said that, if the teacher went over the solution I think it would have been a valuable lesson and well worth spending 20 minutes on. That's really not too much time to spend thinking about a hard (for a 12 year old) problem.

calculo wrote:

Dirtengineer wrote:It took me about 30 seconds

i doubt it...

Why? I'm not that smart and just did it in about the time it took to right these 3 equations down

D=vt

D = 10r + 5(t -R)

(D - 10 r)/5 + r = t

Hmmm I always find distance-time-speed problems confusions especially for younger kids, lots of similar variables.

Took me about 2 min:

Time spent running = R (given by the problem)

Time spent walking = distance walked/walking speed = (D - 10R) / 5

Total time = time spent running + time spent walking =

R + D/5 - 10R/5 = R - 2R + D/5 = D/5- R

gdffdsdagsdf wrote:

3 minutes, but I have a PhD in physics.

how do you get through a phd in physics and not instantly know how to solve that?

Why doubt it? I've spent 4 years in undergrad and 2 in grad school solving all types of word problems. I'm a licensed, practicing civil engineer with a solid background in numerical analysis and a data junkie. I program spreadsheets and python scripts as one of my hobbies. Solving problems is fairly easy when you're familiar with different approaches to problem solving.

Your typical student might be caught up on this problem because they might only be seeing what's stated in the problem and would forget the variable of total time. That's where I think they would get stuck. Solving for T would be the trivial part once you come up with the general equation like I did. I could have reduced further, but I'm lazy.

Writing as I think.

In R hours, I cover 10R km. The remaining distance is D-10R. It takes me (D-10R)/5 hours to walk it (assuming D > 10R, otherwise I run the whole thing). So my answer is R + (D-10R)/5.

It would take a lot longer to think about your question about 12-year-olds. I don't know, the proof is in the pudding, they didn't know the answer. The teacher should have helped guide them with some hints or a warmup problem. For instance s/he could have used actual numbers instead of D and R, lots of people have trouble with variables until they get used to them.

Circular wrote:Why? I'm not that smart and just did it in about the time it took to right these 3 equations down

D=vt

D = 10r + 5(t -R)

(D - 10 r)/5 + r = t

fantastic !

most important considerations are :

brevity/elegance

you madam/sir have taken the biscuit !

3 lines of brilliance !

albeit, how much in 1'38.97 - 3'24.23 range it took you is questionable ?!

kangaroo wrote:

gdffdsdagsdf wrote:

3 minutes, but I have a PhD in physics.

how do you get through a phd in physics and not instantly know how to solve that?

I dunno, it took me about two minutes to decide on the notation I would use, then like half a minute to realize it was ok to leave the answer in terms of R.

Once I had written down the following two lines:

D = 10R + 5W

R+W = ?

Then the rest of the algebra took just a few seconds.

1:38 and 3:24? Aren't those your fantasy times for Jim Ryun's 800 and 1500 prs?

You are full of CRAP. A teacher at a supposed elite school sits back, reads a magazine for 20min and mocks his kids?Do you have nothing better to do than come here on a Fri evening to write this garbage?Dumbazz.

calculo wrote:

i have to check math homework for 12y ole nephew, who is at one of top schools in the State from merit, having won scholarship there

, asked kids to solve it, & sat back reading enquirer for rest of 20'00 in a top school, & after time allotted, laughed when none of the elite 30 kids coud solve it & ridiculed them as they left the class...

why did the teacher call it running when its only 10km/h? That's more like a brisk walk.

Circular wrote:

calculo wrote:

i doubt it...

Why? I'm not that smart and just did it in about the time it took to right these 3 equations down

D=vt

D = 10r + 5(t -R)

(D - 10 r)/5 + r = t

Except that you didn't solve it until your second post. Your first post didn't solve for T, so you didn't actually complete the problem. Look at the time stamp between your two posts, that is how long you took.

Anyway, OP: this problem should be solvable by a gifted 12 year old in intro Algebra in about 5 minutes. Prior to algebra, I would expect very few of them to solve it.

Based on OP's writing skills, I'm glad he is only helping his nephew in math class. On the other hand, if it really took him hours to solve it, maybe he shouldn't be helping him in math. From his post, I really expected it to be a much more complicated problem.

Anyway, if nobody from your nephew's class could solve it, that either means the teacher has failed to teach them what he thinks he has taught them, or he is giving them some sort of a pre-test before they learn this subject.

MBAcurious wrote:

Circular wrote:

Why? I'm not that smart and just did it in about the time it took to right these 3 equations down

D=vt

D = 10r + 5(t -R)

(D - 10 r)/5 + r = t

Except that you didn't solve it until your second post. Your first post didn't solve for T, so you didn't actually complete the problem. Look at the time stamp between your two posts, that is how long you took.

I wasnt the same guy who said it took 30 seconds but if you understand some basic concepts its easy to see the solution. Its actually a great problem for kids but its not just about isolating variables its about figuring out how to approach a problem and find a solution, which is a much more valuable skill. I would say nearly all kids would struggle with this kind of problem at first but with practice could understand it quite easily.

- Dude, love OP, but his posts are like hieroglyphics ... garbled, unreadable, ... an untethered, but gifted mind. Requires a Calculo Filter.

I was expected to and did solve problems very much like that when I was 12. I didn't go to some fancy school, just a run-of-the-mill middle income public junior high. It's a pretty basic and standard Algebra 1 problem.