# Problem on Mathematics - continued

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#### Jenova

##### New Member
After seeing an old thread about mathematics, I would like to post one too...

There are 2 cars, 1km apart travelling towards each other with speed 10km/h until they crash head on. There's a bee that will travel in between the cars at the speed of 20km/h.

How many times can the bee move back and forth between the cars before it got crushed in between?

Assumptions
- The bee can change direction with no time lack and acceleration is neligible.
- The bee's starting point is with one of the cars.

[Car A][Bee]........................................................................[Car B]
..........<---------------------- 1km --------------------------->

V

#### vince123123

##### Guest
Lol, everyone starting to post their homework questions here? HEHE

After seeing an old thread about mathematics, I would like to post one too...

There are 2 cars, 1km apart travelling towards each other with speed 10km/h until they crash head on. There's a bee that will travel in between the cars at the speed of 20km/h.

How many times can the bee move back and forth between the cars before it got crushed in between?

Assumptions
- The bee can change direction with no time lack and acceleration is neligible.
- The bee's starting point is with one of the cars.

[Car A][Bee]........................................................................[Car B]
..........<---------------------- 1km --------------------------->

#### Jia Wang

##### New Member
Couldn't help but try solving it...

I think it's 0.05 hour (180 sec). :bsmilie: Pls correct me if I'm wrong...

#### Astin

##### Senior Member
Couldn't help but try solving it...

I think it's 0.05 hour (180 sec). :bsmilie: Pls correct me if I'm wrong...
Wrong la, the question is how many times...

#### Jia Wang

##### New Member
Wrong la, the question is how many times...
Oops... haha sorry... too excited with the time taken... theoretically this value of 180s is based on an infinite geometric series... but in actual crash, the bee very likely won't survive more than 10 times :bsmilie:

#### tkbonz

##### New Member
LOL...ya it depends on how fat the bee is .... if not quite hard to do and make assumptions to solve.

Anyway, if I'm not wrong, the distance between both cars will be 1/3 of the previous distance in between the time the bee reaches one car to another.

#### satay16

##### Senior Member
Conditions of the problem cannot be met.

......... plus a few smilies to retain the light-hearted humour of this thread.

#### AhSeng

##### New Member
\$50 for an answer. With graphics explaination included. U want?

#### night86mare

##### Deregistered
the way to do this is to use relative velocity

let's say the bee is on the left car

imagine that car two is stationary, the bee will then be moving towards car two at a rate of 30 km/h (20+10)
while car one is moving towards car two at a rate of 10+10 km/h, or rather 20km/h

so what was mentioned earlier is right, everytime the bee reaches another car, the distance remaining is 1/3 of the original before they started moving
this is because everytime it starts from one side, the bee takes 2/3 of the time the two cars need to cover to reach each other to reach the other car due to faster speed

by gp,
first time - 1/3 km distance left
second time - 1/9 km distance left
third time - 1/27 km distance left
fourth time - 1/81 distance left

and so and so forth

so this is a stupid question, since even when distance between the two are minutely small, the bee is flying faster than the two cars' relative motion to each other.
even if distance left is 0.01cm between the two when the bee has reached one of the two cars, the bee is just buzzing very fast in between the two

answer is simply related to the amount of time taken for the two cars to meet, i.e. 1/20 hour or 3 minutes. because once they meet, confirm the bee gone case.
in this three minutes, the bee can only fly 20/20 km = 1 km. because it is travelling at constant speed.

but if you want the number of times the bee is going to be able to move back and forth in between, amazingly, it seems like the answer is infinite.

#### richardg

##### New Member
After seeing an old thread about mathematics, I would like to post one too...

There are 2 cars, 1km apart travelling towards each other with speed 10km/h until they crash head on. There's a bee that will travel in between the cars at the speed of 20km/h.

How many times can the bee move back and forth between the cars before it got crushed in between?

Assumptions
- The bee can change direction with no time lack and acceleration is neligible.
- The bee's starting point is with one of the cars.

[Car A][Bee]........................................................................[Car B]
..........<---------------------- 1km --------------------------->
guess infinite?

#### night86mare

##### Deregistered
guess infinite?
you is copy my answer !

:kok:

:bsmilie::bsmilie:

#### richardg

##### New Member
you is copy my answer !

:kok:

:bsmilie::bsmilie:
aiyoh sollie forgot to check first..

haha its one of those each time the distance is halved puzzle
when will the twain meet?

#### night86mare

##### Deregistered
haha its one of those each time the distance is halved puzzle
when will the twain meet?

:bsmilie:

#### rvxing

##### New Member
Can be infinite only if the bee size is 0, so infinite is not the answer. The answer can only be known if the size of bee is known, just as the others already mentioned.

#### richardg

##### New Member
Can be infinite only if the bee size is 0, so infinite is not the answer. The answer can only be known if the size of bee is known, just as the others already mentioned.
still infinite
provided size of bee < 1km...:bsmilie:

a bit like fractals in reverse..
universe can be as big and as small

#### night86mare

##### Deregistered
still infinite
provided size of bee < 1km...:bsmilie:

a bit like fractals in reverse..
universe can be as big and as small
yes

the fact is relative velocity of bee to two cars is still faster.

just when it's going to get squished, that's it's moment of glory, it will bounce between the two like a bat out of hell :bsmilie:

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