[Guest]

4 quick math puzzles:

(some of these probably exist in similar variations, but hardly in the same versions)

#1

Two friends are driving in the same car together from one city to another.

Going out, Adam drives for 50 kilometers, and Brian drives the rest of the way.

Returning home on the exact same route Adam drives some distance, and Brian drives the remaining 60 kilometers.

Who is driving the greatest distance, and how much longer than the other person is he driving?

#2

Abigail died 120 years after Bethel was born.

The sum of their ages at death was exactly 100 years.

Bethel died in the year 40 BC

In what year was Abigail born?

#3

You are standing on a train platform, which is 110 metres long.

A train approaches from the right and it passes you in exactly 6.3 seconds.

The train passes the entire platform in 10.7 seconds.

How long is the train ?

#4

Adam and Brian are now in their respective home towns, which are directly connected by a highway.

Each of them simultaneously get the bright idea that they will pay the other friend a surprise visit.

Adam and Brian set out in their own cars at the same time driving towards the other friend's town. They are driving at different speeds - but both at a completely uniform pace (ie. no delays for stopping/starting, always maintaining the same speeds etc.).

precisely 360 kilometers from Adam's town the friends discover eachother as they are passing by. Both are annoyed by the fact that the other friend had the same idea and now wont be home. Equally annoying is the fact that there are no exits on the highway except for their respective home towns.

Each friend reach the town of the other friend at different points in time, and immediately hereafter turn around, and drive back towards their own home towns hoping to find the other friend still waiting there.

Both are even more frustrated as they pass eachother again, this time precisely 240 kilometers from Brian's town.

As stated they both keep their initial pace throughout the trip. And they both spend the same amount of time switching direction on the highway at the towns.

What is the exact distance between Adam's and Brian's towns?

[Guest]

The first two seem to me to be impossible to solve as there isn't enough information.

The third one is like some schoolboy maths problem, which I have taught when I was in India. This needs simultaneous equations about the train speed and length.....

The fourth is in similar vein .....I think

[Guest]

The first two seem to me to be impossible to solve as there isn't enough information.

The third one is like some schoolboy maths problem, which I have taught when I was in India. This needs simultaneous equations about the train speed and length.....

The fourth is in similar vein .....I think

Well... things are not always what they appear

None of these puzzles are impossible to solve - schoolboy or not.

[Guest]

I've done the fourth one after confusing myself unnecessarily a few times

Using the ratios of the speeds and simplifying the distances to 3 and 2 gave me the answer 7, which, when multiplied by 120 is 840. This checks out.

[Guest]

OK, I've solved the age problem. It wasn't impossible.

I thought it may be something to do with there being no year zero between BC and AD, but that was only a distraction!

Abigail was born in 20 BC. solved with a bit of algebra.

[Guest]

I think these are the answers for 1 and 2

#1

Brian drives 20 km more than Adam

#2

20 BC

[Guest]

I've done the fourth one after confusing myself unnecessarily a few times

Using the ratios of the speeds and simplifying the distances to 3 and 2 gave me the answer 7, which, when multiplied by 120 is 840. This checks out.

While the answer is correct it would be nice to see a solution that would work also for numbers that are not even. This is more of a trial-and-error based guess.

[Guest]

OK, I've solved the age problem. It wasn't impossible.

I thought it may be something to do with there being no year zero between BC and AD, but that was only a distraction!

Abigail was born in 20 BC. solved with a bit of algebra.

...and algebra should solve it. Would you care to include your algebra in the spoiler so that others might learn from it?

I know I didn't ask this in the OP... my mistake I guess.

[Guest]

I think these are the answers for 1 and 2

#1

Brian drives 20 km more than Adam

#2

20 BC

Both answers are correct. Again... the proof of the answers would be nice to have included.

[Guest]

For #1

going: Total Distance = 50 + B1

return: Total Distance = A2 + 60

eqating these both gives B = A + 10 (on each way) i.e B drives 20 Kms more then A for whole trip.

#2

Date of death of B = 40

Date of birth of B = 40 + B (in BC date of birth is more then date of death)

Date of death of A = 40 + B - 120

Date of birth of A = (40 + B - 120) + (100 -B) (taking in consideration that total of their ages was 100)

= 20 BC

#3

Length of train = x

speed of train = x/6.3 (it passes a single point in 6.3 secs)

total distance to be covered for passing platform = 110 + x

time taken = 10.7

speed of train = (110+x)/10.7

x/6.3 = (110+x)/10.7

x = 157.5 meters

Hope I am right

[Guest]

...

[unmasked spoilers removed]

...

Let me start by saying: "Welcome to BrainDen".

There are 2 perfectly logical reasons that I assume you are a new member:

1) It's says you created 1 post before

2) You failed to hide your answers in the 'Spoiler' sections, which may cause new visitors to involuntarily see the answers before solving them.

That being said; all 3 answers are correct and nicely explained.

You will find the 'Insert: Spoiler' button/bar when composing a post/reply.

Answer will only be shown if I choose to click here...

Edited April 4, 2009 by uhre

[Guest]

#4

x is the total distance between the homes

Adams speed =(360)/t1=(x+240)/t2

Brian's speed=(x-360)/t1=x+(x-240)/t2

so for Adam t1/t2=360/(x+240)

for Brian t1/t2=(x-360)/(2x-240)

Equating the two t1/t2 equations...

360/(x+240)=(x-360)/(2x-240) crossmultiply to get

720x-86400=x^2 -360x+240x-86400

840x=x^2

x=840

[Guest]

#4

x is the total distance between the homes

Adams speed =(360)/t1=(x+240)/t2

Brian's speed=(x-360)/t1=x+(x-240)/t2

so for Adam t1/t2=360/(x+240)

for Brian t1/t2=(x-360)/(2x-240)

Equating the two t1/t2 equations...

360/(x+240)=(x-360)/(2x-240) crossmultiply to get

720x-86400=x^2 -360x+240x-86400

840x=x^2

x=840

Absolutely correct.

[Guest]

While the answer is correct it would be nice to see a solution that would work also for numbers that are not even. This is more of a trial-and-error based guess.

I didn't put all the maths in as I didn't want to spoil it completely for anyone needing a little help.

On the first leg, A travels 360 Km and B travels x - 360 Km (where x is the distance between the towns)

On the completion of the second leg, A has travelled x + 240 Km and B has travelled 2x - 240 Km.

The speeds are constant, so the ratios of distance travelled by A and B can be equated.

So 360 / (x - 360) = (x + 240) / (2x - 240)

This gives 720 x - 360 . 240 = x2 - 120 x - 360 . 240

Simplifying gives 720 x = x2 - 120 x ; so x = 0 or 840

So, either the towns are no distance apart, or they are 840 km apart.

Does that make sense?

Edited April 4, 2009 by donjar

[Guest]

Problem number 1

Thanks for the solution, but I maintain that the original problem is insoluble. The second part of the question is:

how much longer than the other person is he driving?

Since we know nothing about the total distance or speed, we can't say anything about the TIME that each person spends driving.

Edited April 4, 2009 by donjar

[Guest]

Problem number 1

Thanks for the solution, but I maintain that the original problem is insoluble. The second part of the question is:

how much longer than the other person is he driving?

Since we know nothing about the total distance or speed, we can't say anything about the TIME that each person spends driving.

Well, it is one of those problems that appear to be unsolvable, but it actually isn't. This is proven fairly easy. The thing is, that you don't really need to know anything about the total distance, speed or time taken. You are only asked about the distance driven relative to eachother - and that information is given in the puzzle.

They drive from A to B : total distance = x

Out: Adam drives 50 kilometers and Brian the rest (x - 50)

Return: Brian drives 60 kilometers and Adam the rest (x - 60)

So Adam drove: 50 + (x - 60) = x - 10

Brian drove: (x - 50) + 60 = x + 10

It should now be quite obvious that even if we don't know how far the distance x is, we know that Adam drove 20 kilometers less than Brian.

[Guest]

It seems the problam Donjar has with #1 is the English used in the second part of the question.

Uhre, I think the point Donjar is trying to make, is that the OP says "how much longer than the other person is he driving?" that leaves an uncertainty about the answer required; is it distance or time. No from the info given one should logically assume that it is distance. However the common usage of English could easily lead one to assume a time is wanted. (e.g. how much longer 'til we get there? One would usually expect an answer in hours and minutes not km.) A better way to phrase it would be "how much further than the other person is he driving?" as this elimates the ambiguity. I'm not being faceious just trying to show you where I think Donjar is coming from.

Dan