## Saturday, July 25, 2009

### Alin and Motti's Sunday Trip

One Sunday, Alin (the greatest puzzle solver of all times) and his friend Motti decided to go for a ride in the countryside. One rode a bicycle and the other a motorcycle. Sometime into their trip, a storm started and both had to call Motti's grandma to come to the rescue. When grandma came to pick up Motti, she noted that if he had ridden three times as far as he had, he would be two times as far to the start as he is to the finish. When she picked up Alin, she noted that if he had ridden half as far as he had, he would have three times as far to ride as he had.
Who rode the motorcycle?

Submit your answer on our Family Puzzle Marathon site. Solve three puzzles and get a prize!

Alin Grin said...

I

Maria said...

You may be right, but you have to prove it.
Motti may claim the same....
Drawing or equation, whatever works.
You can email me the drawing and I will post it within the puzzle.

Anonymous said...

if this is a tricky question then the answer is 'No one rode the motorcycle' ... because of the 'one rode a bike and ANOTHER (instead of "the other") rode the motorcycle.
If this is a math question than ... you might want to rephraze 'twice further away from the start than to the finish' ... feels like it's missing somthing :-)

Maria said...

Math is a precise science, so thanks for pointing out the language imprecisions. English is not my first or even second language and I am therefore not able to feel these misstatements that otherwise scream into a native's ear. I will try to rephrase these few sentences as you suggested.
The answer is still for grabs.
Who can beat Alin in providing a solution?

rachel_t said...

Assuming the length from start to finish is the same for the two, that distance is D

m = distance Motti traveled
3 m = (2/3) D

a = distance Alin traveled
(1/2) a = (1/4) D

in Motti's case,
D = (9/2) m

in Alin's case
D = (4/2) a = 2 a

(9/2) m = 2 a

m = (4/9) a

Alin traveled farther, so he's probably the one who rode the motorcycle.

Maria said...

Yes!
Rachel T rules and gets above the 10 puzzle mark.

There is actually another graphical solution to this puzzle that may be simpler.
Draw two intervals of the same length - this is Alin and Motti's planned trip length.
Divide one interval into 4 equal parts. Alin has been picked up when he was right in the middle of his trip. (check - if he had ridden half as far as he had, he would have three times as far to ride as he had)
Divide another interval into 9 equal parts. Motti was picked when he finished 2 out of these 9 steps. (check - if he had ridden three times as far as he had, he would be two times as far to the start as he is to the finish)

As 2/9 of the interval is less than 1/2, Motti is behind Alin. So, Alin is using the faster vehicle - a motorcycle.