A bit of fun, see if you need a tutor? (1 Viewer)

[oasfree]

I found a little math problem from an old selective school test. Let's see if you smart kids out there can solve this grade 5-6 problem. If you cannot, perhaps you need tutoring, otherwise you just do well by self-learning
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Anna walks to school in 20 minutes. Anna can cycle to the school in 5 minutes. How much faster can Anna cycle than walk?
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This was a real question. The wording was so confusing in this sentence "How much faster can Anna cycle than walk?". So I rewrite the question to make it completely clear. This is the question I'd like people to try.
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Anna walks to school in 20 minutes. Anna can cycle to the school in 5 minutes. How many times faster can Anna cycle than walk?

I gave this question to many people in Australia and the USA on answers.yahoo.com, most of the adults and kids failed to solve it properly. So be warned, it's not as naive as it looks even after I have removed the English ambiguity from it. It's an algebraic question requiring critical thinking even though it looks like a very plain every day kiddy problem.

Have fun!

 

[jellybelly08]

Anna walks to school in 20 minutes. Anna can cycle to the school in 5 minutes. How many times faster can Anna cycle than walk?

She can cycle 15mins faster, so 3*faster than she walks.

 

[georgefren]

I dont get it.

If we let the distance be x, then

walking speed = distance/time
= x/20

cycling speed = distance/time
= x/5

Her cycling speed is (x/5)/(x/20) = 4.

theres no way around it. The wording of 'faster' should not matter, because she cycles at 4 times her speed of walking.

Surely the wording of the question of "how many" shouldnt change the relative speed.

 

[study-freak]

I found a little math problem from an old selective school test. Let's see if you smart kids out there can solve this grade 5-6 problem. If you cannot, perhaps you need tutoring, otherwise you just do well by self-learning
---
Anna walks to school in 20 minutes. Anna can cycle to the school in 5 minutes. How much faster can Anna cycle than walk?
---
This was a real question. The wording was so confusing in this sentence "How much faster can Anna cycle than walk?". So I rewrite the question to make it completely clear. This is the question I'd like people to try.
---
Anna walks to school in 20 minutes. Anna can cycle to the school in 5 minutes. How many times faster can Anna cycle than walk?

I gave this question to many people in Australia and the USA on answers.yahoo.com, most of the adults and kids failed to solve it properly. So be warned, it's not as naive as it looks even after I have removed the English ambiguity from it. It's an algebraic question requiring critical thinking even though it looks like a very plain every day kiddy problem.

Have fun!

still ambiguous. Does the speed refer to average speed or instantaneous speed? If former, 3 times faster(edited after looking at the answer lol), if latter, cannot be inferred, and also this question assumes that Anna starts from the same location and follows the same paths to school, none of which is mentioned.. should it be assumed?

(just trying to be critical)

 

[georgefren]

wait ...

walking- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
cycling - - 1..........2............. 3......................4.......................5

she travels at give times the speed.

although i dont get how that works with the maths.

 

[oasfree]

Just as I expected. This problem was in a selective school test for kids at early year 6. The kids get 40 questions to be completed in 40 minutes. A problem like this only allow them 2-3 minutes to think. And often the most intuitive thing that appears in mind is the wrong answer. It's tough! This problem hits hard on critical usage of English in math & science. The generic problem is further complicated by the relation of distance, time and speed. In short, it's a very obvious practical problem that looks simple but very hard to hit it right on the head. So many people have got it wrong. Even those who got it right, did not really got it "completely" right. Many got it right for the wrong reasoning that just happens to hit the right answer. I hope some of you guys who did not get it right will some how use it to test your math teachers to see if they have critical thinking in their mind or just cycling through textbook formulas. If they get it wrong too, let's pray to God to fix our education system.

Let's wait a little longer for a few more people to try. Then I will show the algebraic work leading to a complete answer. It would be an interesting example of how you can use a tool like algebraic logic to arrive at a bullet-proof solution rather than a hit-and-miss general reasoning or guessing. It took me 2 minutes to guess the correct answer but it took 15 minutes to prove that my answer was completely correct (and perhaps mathematically beautiful).

 

[study-freak]

lol I got it.. looked at answers.yahoo.com

that question was ridiculous

 

[oasfree]

She can cycle 15mins faster, so 3*faster than she walks.

Have a think again! She did not cycle 15mins faster. She saved 15 minutes by cycling. Know what I mean when I say it's confusing just by looking at the plain English comprehension.

 

[arjungamer123]

walking speed:
x/20

cycling speed:
x/5

therefore, to equate the speeds, you'd need to multiply the walking speed by 4 to achieve the same cycling speed:

4 times x/20
=
x/5

Therefore, 4 times faster.

EDIT: x is any arbitrary number which denotes the distance aht anna cycles.

No?

 

[oasfree]

lol I got it.. looked at answers.yahoo.com

that question was ridiculous

Oh, please! Don't look at my previous tussle with US guys! BTW, what I provided wasn't the completely mathematically correct answer. In fact it was more of the wrong way that arrived at the right answer. I promise to give a beautifully mathematically correct algebraic solution. So please wait. Just try to solve it by digging deeper. This is the beauty of critical thinking. How do you think Federer made masterful stroke to separate himself from the rest of the tennis crowd? It's his discipline, practice, coolness added into a stroke of genius. I appeal to people to think of math as something quite beautiful

 

[oasfree]

walking speed:
x/20

cycling speed:
x/5

therefore, to equate the speeds, you'd need to multiply the walking speed by 4 to achieve the same cycling speed:

4 times x/20
=
x/5

Therefore, 4 times faster.

EDIT: x is any arbitrary number which denotes the distance aht anna cycles.

No?

Surely a better attempt to address the question showing some valid relationships. But sorry, no. You answer another question that wasn't asked for! Again, blood critical thinking is required here. Many adults out of their black heart have called selective school students as hard-working morons who only know how to use formulas and being incapable of thinking. If these young kids "really" get this one right, I would take my hats off to salute them.

 

[Takuto]

anna cycles 300% faster than she can walk

no mathematics required ftw LOL

nvm just read the other question, how many times. even though it wasnt teh original.. u still would be able to say 4x AS fast and that would be right wouldn't it..

i still dont see how this riddle crap proves ur smart hah.

 

[oasfree]

Hey, the tutors and colleges that advertise here should try this question too! Don't look for my analysis of it posted on the Internet. It might even misled you. Some even claim that they can help 70% of their kids to get into selective schools. Try to solve this real selective school test question properly. I don't mean just pick or guess a correct answer. I mean solve it correctly by giving a bullet proof solution. There are more than 1 way to do this. I think if we wait a while, some tough kids on 3u-4u extension will crack this problem easily. But if these kids have gaps in early learning, they may find this little problem very difficult to hit on the head.

 

[oasfree]

anna cycles 300% faster than she can walk

no mathematics required ftw LOL

nvm just read the other question, how many times. even though it wasnt teh original.. u still would be able to say 4x AS fast and that would be right wouldn't it..

i still dont see how this riddle crap proves ur smart hah.

It's not a riddle. It's a real question from selective school test for year 6. It's not about being smart. No one is trying to be smart here. I would like to see if any one here can completely solve this problem providing a bullet proof solution.

Can you show the proof that support your answer? Perhaps you are one of those who got the right answer by following the wrong trail. As I said before, my suggestion posted on the Internet a while ago was pretty much about hitting the right answer with wrong reasoning.

 

[oasfree]

I dont get it.

If we let the distance be x, then

walking speed = distance/time
= x/20

cycling speed = distance/time
= x/5

Her cycling speed is (x/5)/(x/20) = 4.

theres no way around it. The wording of 'faster' should not matter, because she cycles at 4 times her speed of walking.

Surely the wording of the question of "how many" shouldnt change the relative speed.

You are so close. Your reasoning is clear. But you say "The wording of 'faster' should not matter". This is what's wrong. It does matter as far as the author of this question was concerned (all selective school tests are prepared by ACER in contract with the NSW DET). I know a lot of people know the answer but I am looking for a little more, the ability to show a completely correct proof to back up the answer.

 

[Takuto]

Many adults out of their black heart have called selective school students as hard-working morons who only know how to use formulas and being incapable of thinking. If these young kids "really" get this one right, I would take my hats off to salute them.

i was referring to this hhah. and the fact it uses tricks based on english makes it a riddle not a pure mathematics question. lol

i didnt feel the need to show working as others already did it.. What I don't get is why '4x as fast' is a flawed answer.

u dont use the word faster, therefore do not need to say 3x faster (which i assume is the 'right answer')

 

[Lazarus]

I think georgefren and Takuto have reasoned out the answers to both variants of the question. Dealing with the second variant first...

Anna walks to school in 20 minutes. Anna can cycle to the school in 5 minutes. How many times faster can Anna cycle than walk?

We all know: [maths]d=st[/maths]

In this case, the distance is the same whether she walks or cycles, but the speeds and times differ, so:

[maths]d=s_{w}t_{w}[/maths]

[maths]d=s_{c}t_{c}[/maths]

Thus:

[maths]s_{w}t_{w} = s_{c}t_{c}[/maths]

[maths]20s_{w} = 5s_{c}[/maths]

[maths]s_{c} = 4s_{w}[/maths]

This means that her average cycling speed is equal to four times her average walking speed.

As georgefren said, I think this has to mean that the answer is that she can cycle four times faster than she can walk.

Anna walks to school in 20 minutes. Anna can cycle to the school in 5 minutes. How much faster can Anna cycle than walk?

I don't think I would have picked up on the ambiguity in the question if oasfree hadn't explicitly mentioned it and Takuto hadn't provided his solution.

But as Takuto observed, "how much faster" is (arguably) looking for the same answer in a different form.

The percentage by which her speed is increased when she is cycling is given by:

[maths]x=\frac{s_{c}}{s_{w}}%2A100[/maths]

Substituting [maths]s_{c}[/maths] from the previous question:

[maths]x=\frac{4%2As_{w}}{s_{w}}%2A100[/maths]

[maths]x=4%2A100[/maths]

[maths]x = 400[/maths]

So Anna can cycle 400% faster than she can walk.

Actually this seems to be what georgefren did too.

 

[omniscience]

op is fucking stupid.

if you don't get it, it just means that you need to study harder not get a tutor. tutor doesn't solve everything,

 

[georgefren]

oasfree, the selective schools test does not require algebraic thinking.

in fact, i didnt even learn algebra until about year 8.

if you actually have an answer, your not allowed to use algebra to prove it because people in the test shouldnt need to use algebra in order to solve the problem.

 

[addikaye03]

OP, post ur solution. I thought it seems pretty bloody straight forward.
I did exactly what Lazarus did:S