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# Russian Problems

## Question

these are some problems from a Russian puzzle book. I've adapted and changed them a little bit...

1) Bob is going on a journey. For the first half he takes a horse cart, which goes 3 times faster than he can walk. For the second half he took an oxen cart, which goes half as fast as he can walk. Would he have gone faster or slower if he had walked all the way on foot? And how much time is saved for the faster way?

2) Randy's pals ask him how many kittens he has. His answer was: "Three-quarters of their number plus three-quarters of a kitten." His pals laughed at the joke, but it wasn't a joke... and he doesn't have any chopped up kittens either. How many kittens does he have?

3) There are 12 flags at an ancient Olympic race. The runners start at the first flag of course. A certain runner has the same speed and stride all the way throughout the race. When he got to flag 8, four seconds had gone by. How many seconds did it take for him to finish the race?

4) Two bikers are 180 miles apart and going toward each other on a straight line. They are biking steadily at 15 mph. A fly (going 30 mph) is flying constantly in between them. When it reaches the next biker, it turns around and goes back to meet the next biker, etc. When the bikers meet and the fly stops flying, how many miles has the fly flown?

5) A bus leaves Manhattan to go to Queens at noon. A biker leaves Queens to go to Manhattan an hour later, and the biker is going 15 mph slower than the bus. When they meet, which is farther from Manhattan?

6) The toy costs \$1 plus half its price. How much does it cost?

I hope these haven't already been posted...

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for problem 1) It takes more time to complete the journey using the horse and oxen carts compared to walking. i.e. if the two part journey takes 60 minutes walking. the first part would take you 10 minutes on the horse cart (30/3=10). the second part would take you 60 minutes since you are going half your speed (30*2=60). so using the carts take you 70 min vs.

for problem 2) Randy has 3 kittens. let x be the number of kittens. (3/4)x + (3/4) = x

(3/4)= x - (3/4)x

(3/4) = (1/4)x

(3/4)/(1/4)=x

x=3

for problem 3) if the distance between flags is the same, and the time to go from one flag to the next is the same, and if the race end at the 12th flag, then it takes (44/7) seconds which is around 6.285 secs

for problem 3) the toy costs 2 dollars.

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yeah u figured out the catch in problem 3, which was ur starting at 1, not 0, so u have 11 flags to go, not 12, and flag 8 is actually the seventh flag you reach. Good job!

yes for problem 1, just the oxen cart takes up the whole time it wouldve taken to walk, and the time saved by walking is whatever time you took for the first half

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(4) and (5) have catches too

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(4) and (5) have catches too

yeah I know, I just hate those problems where someone meets another one at the other side of the road, also upon ready the fly problem i think is impossible to maintain a constant speed because you have to accelerate pretty fast when turning the other way and keep up with speed.

anyway just don't like those problems. LOL

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i'll post the answers for 4 and 5 (6 is easy):

Way easier than it looks: the bikers are going the same speed so they meet after they have both gone 90 miles. 90m/15mph = 6 hours to meet each other. That just means the fly was flying constantly for 6 hours. 6x30 = 180 miles. The fly flew 180 miles total while going back and forth.

When they meet, they are in the exact same place. Neither is farther from Manhattan! I love this trick question!

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Technically, the biker will be further since when they meet, the biker's back end will extend further away from Manhattan:P

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these are some problems from a Russian puzzle book. I've adapted and changed them a little bit...
1) Bob is going on a journey.

For the first half he takes a horse cart, which goes 3 times faster than he can walk.

For the second half he took an oxen cart, which goes half as fast as he can walk.

Would he have gone faster or slower if he had walked all the way on foot?

And how much time is saved for the faster way?

The time for the oxen cart half of the journey = the time had he walked all the way on foot.

The time penalty is thus the time for the horse cart, which is 1/6 of the time for walking all the way on foot.

2) Randy's pals ask him how many kittens he has.

His answer was: "Three-quarters of their number plus three-quarters of a kitten."

His pals laughed at the joke, but it wasn't a joke... and he doesn't have any chopped up kittens either.

How many kittens does he have?

Three quarters of his friends must be a whole number plus one-fourth, so that adding three-fourths gives a whole number of kittens.

The simplest answer is 3 friends, 3 kittens.

You can add multiples of 4 friends and 3 kittens to get other answers.

3) There are 12 flags at an ancient Olympic race.

The runners start at the first flag of course.

A certain runner has the same speed and stride all the way throughout the race.

When he got to flag 8, four seconds had gone by.

How many seconds did it take for him to finish the race?

He has passed 7 flags in 4 seconds.

The entire race would take him [11/7] x 4 seconds = about 6.286 seconds

4) Two bikers are 180 miles apart and going toward each other on a straight line.

They are biking steadily at 15 mph.

A fly (going 30 mph) is flying constantly in between them.

When it reaches the next biker, it turns around and goes back to meet the next biker, etc.

When the bikers meet and the fly stops flying, how many miles has the fly flown?

The bikers will meet in 180/30 = 6 hours.

The fly will have flown 6x30 = 180 miles by then.

5) A bus leaves Manhattan to go to Queens at noon.

A biker leaves Queens to go to Manhattan an hour later, and the biker is going 15 mph slower than the bus.

When they meet, which is farther from Manhattan?

If they meet by having the front end of the bus contact the front part of the biker, the bus will be closer to, and the biker will be farther from, Manhattan.

If they are treated as point objects, they will of course be equidistant from Manhattan.

By the way this is an impossible problem: in normal Manhattan traffic, the biker will travel faster than the bus.

6) The toy costs \$1 plus half its price. How much does it cost?

\$2. \$1 must equal half its price.

I hope these haven't already been posted...

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I think I had to reread 5 about 100 times before I got it. I was getting really pissed off that I was the only person that didn't treat the distance between Manhatten and Queens as common knowledge.

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for problem 1) It takes more time to complete the journey using the horse and oxen carts compared to walking. i.e. if the two part journey takes 60 minutes walking. the first part would take you 10 minutes on the horse cart (30/3=10). the second part would take you 60 minutes since you are going half your speed (30*2=60). so using the carts take you 70 min vs.

for problem 2) Randy has 3 kittens. let x be the number of kittens. (3/4)x + (3/4) = x

(3/4)= x - (3/4)x

(3/4) = (1/4)x

(3/4)/(1/4)=x

x=3

for problem 3) if the distance between flags is the same, and the time to go from one flag to the next is the same, and if the race end at the 12th flag, then it takes (44/7) seconds which is around 6.285 secs

for problem 3) the toy costs 2 dollars.

how can the toy cost 2 dollars? wouldnt it be 1.50?
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no, it's simple math.

1+.5x = x

it follows that 1 must be half of x. Therefore x is \$2. You fell for the catch of the riddle, geniusman

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1. Let us consider the distance is 12 km. Bob's speed is 2km/hr. So on horse cart he went 6 km in 1 hr. on ox cart he went 6 kmin 6 hr. Total-->7hr. On foot Total-->6hr. So, he could have gone faster in second method (on foot). he could have saved 1/7th of total time of first travel.

2. 3 kittens. (3*3/4+3/4)=3

3. As one flag is at the beginning, So he passed 7/11 of total distance in 4 seconds. So total time taken is 4*11/7=2*pi seconds <_<

4. The bikers met after 6 hrs. So, the fly flies for 6 hrs---6*30=180 km

5.They met in same distance from manhattan.

6. 2\$ (1+2*1/2)=2.

Edited by storm
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for problem 1) It takes more time to complete the journey using the horse and oxen carts compared to walking. i.e. if the two part journey takes 60 minutes walking. the first part would take you 10 minutes on the horse cart (30/3=10). the second part would take you 60 minutes since you are going half your speed (30*2=60). so using the carts take you 70 min vs.

in question 1 if he walks at 1mph then the first half would be 3miles and the second would be .5 miles=3.5miles in 2 hours. walking 3.5 miles would take 3.5 hours therefore he saves 1.5 hours not walking.

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these are some problems from a Russian puzzle book. I've adapted and changed them a little bit...

1) Bob is going on a journey. For the first half he takes a horse cart, which goes 3 times faster than he can walk. For the second half he took an oxen cart, which goes half as fast as he can walk. Would he have gone faster or slower if he had walked all the way on foot? And how much time is saved for the faster way?

In question 1 you did not specify what was halved the distance or the time of the journey. Therefore if he walks at 1mph then the first half would be 3miles and the second would be .5 miles=3.5miles in 2 hours. walking 3.5 miles would take 3.5 hours therefore he saves 1.5 hours not walking.

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The problem only addresses Speed and Time.

X = walking speed

3X = horse cart speed

0.5X = oxen cart speed

Y = Time traveled

Walking: X*Y

Horse/Oxen: (3X*(Y/2))+(0.5X/(Y/2))

X=3,Y=2

Walking: 3*2=6

Horse/Oxen: ((3*3)*(2/2))+((0.5*3)/(2/2))

(9*1)+(1.5/1)

9 + 1.5 = 10.5

X=6,Y=4

Walking: 6*4=24

Horse/Oxen: ((3*6)*(4/2))+((0.5*6)/(4/2))

(18*2)+(3/2)

36 + 1.5 = 37.5

Edited by lords8n
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i didnt look at post so correct me if im wrong

walk

3 =2.25+0.75

(4/(8-1))x(12-1)=6.286

Spoiler for Qu4:

0 miles because its constantly in between them so it cant go anywhere

he starts at 1 not 0

no ones further coz they meet at the same point, same distance from Manhatten

\$1 coz it only asks you how much it costs not the total

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how can a fly travel if its constantly between them

the bus and the bike meet at 1 place, no matter where it is its the same distance from anywhere

no logic on Qu6

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I was looking at the member online list thing, and saw someone looking at this. The problems seemed so easy, of course I had to solve them all. Since the topic's over a year old, I'm sure all the answers are here, but I'll post mine anyway. I haven't looked at anyone else's since I'm pretty confident in mine.

1. Let's say the journey is 3 miles and Bob walks at 1 mph.

So... With cart... Half the journey.. 1.5 miles in 30 minutes

With oxen thing............................... 1.5 miles in 3 hours

It's faster if Bob walked the whole thing (3 hours total, 30 minutes faster). By walking, Bob saves 10 minutes for every miles he travels.

2. 3 kittens. 3 * .75 = 2.25 + .75 = 3.

3. 6 seconds. He does 1 flag in half a second.

6.286 seconds. If he starts at the first flag, then he only runs for 11 flags.

4. ...Umm, this reminds me of Bonanova's robot problem. I'm just gonna go with my gut and say 180 miles, with no real math to back it up.

5. Well, if they meet they're the same distance from Manhattan. Unless you mean meet "face to face", in which case the bust would be as it's longer and the end will be slightly closer...

6. So... let's let the price be x.

1 + .5x = x

1 = .5x

2 = x

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these are some problems from a Russian puzzle book. I've adapted and changed them a little bit...

...

5) A bus leaves Manhattan to go to Queens at noon. A biker leaves Queens to go to Manhattan an hour later, and the biker is going 15 mph slower than the bus. When they meet, which is farther from Manhattan?

...

Why does the Russian puzzle book feature Manhattan and Queens instead of the Red Square and Profsouznaya street? Or, at least, the Brighton Beach?

By the way, I saw this one problem in a Russian puzzle book for the 3rd -5th grades some 40 years ago, but it used steam boats leaving the harbors A and B.

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1. faster by 1/6 of the walking total time

2. 3 kittens

6. \$2

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(4) and (5) have catches too

1) The combination of horse and oxen cart will take 1/6th of time more than the walking way

2) 3 kittens

3) 44/7 seconds

4) 180 miles

5) Both will be at the same distance when they meet, obviously.

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"Bob is going on a journey. For the first half he takes a horse cart, which goes 3 times faster than he can walk. For the second half he took an oxen cart, which goes half as fast as he can walk. Would he have gone faster or slower if he had walked all the way on foot? And how much time is saved for the faster way?"

Answer: slower. by 1/4 of the speed

3 * x/2 +  -1/2 x/2

= 3/2 x - 1/4 x
= x( 6/4 - 1/4)
= x (5/4)
so 1/4 speed faster if Bob took the faster way via his trusty animals :)
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4 hours ago, CCC said:

"Bob is going on a journey. For the first half he takes a horse cart, which goes 3 times faster than he can walk. For the second half he took an oxen cart, which goes half as fast as he can walk. Would he have gone faster or slower if he had walked all the way on foot? And how much time is saved for the faster way?"

Let x = time taken to travel by foot.
So via animals = 1/3 * x/2 + 2 * x/2
= 1/6 x + 2/2 x
= x(1/6 + 1)
= x (7/6)
so 1/6 slower if he took the animals

On 5/1/2008 at 1:51 AM, Guest said:

The problem only addresses Speed and Time.

X = walking speed

3X = horse cart speed

0.5X = oxen cart speed

Y = Time traveled

Walking: X*Y

Horse/Oxen: (3X*(Y/2))+(0.5X/(Y/2))

X=3,Y=2

Walking: 3*2=6

Horse/Oxen: ((3*3)*(2/2))+((0.5*3)/(2/2))

(9*1)+(1.5/1)

9 + 1.5 = 10.5

X=6,Y=4

Walking: 6*4=24

Horse/Oxen: ((3*6)*(4/2))+((0.5*6)/(4/2))

(18*2)+(3/2)

36 + 1.5 = 37.5

Let x = time taken to travel by foot.
So via animals = 1/3 * x/2 + 2 * x/2
= 1/6 x + 2/2 x
= x(1/6 + 1)
= x (7/6)
so 1/6 slower if he took the animals

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