[Guest]

Not sure if any version of it has been posted earlier...could not find any with the search though.

The Monster Moose set out at noon to walk from Moose County to Banishire, and the Bani-rabbit started at 2 p.m. on the same day to walk from Banishire to Moose County. They met on the road at five minutes past four o'clock, and each of them reached their destination at exactly the same time. Can you say at what time they both arrived?

Don't forget the spoiler

[unreality]

were they traveling at constant speeds?

[Guest]

were they traveling at constant speeds?

Yes we can assume that.

[Guest]

4:05

[Guest]

I'm still missing a piece of information I think.

I get three ways of expressing the total distance:

D = speed of rabbit x time of rabbit

D = speed of moose x (time of rabbit + 120 mins)

D = (speed of rabbit x 245 mins) + (speed of moose x 125 mins)

We want the time of rabbit to solve, but are missing an equation unless we know the distance too.

Presumably I'm missing something obvious.

obviously it works if Moose County and Banishire are the same place. They both go for a walk on a "circular" route that takes them back to their starting point, and both finished at exactly 4.05pm.

But then they're more likely to meet in the pub after their walk, rather than on the road!

[TwoaDay]

Edit: deleted everything, i read the problem wrong

Edited July 28, 2008 by TwoaDay

[Guest]

Seven o'clock

Making the assumption that Moose County and Banishire are not the same place, we can assign values to the given variables. Also, because they meet at the same place and arrived at the same time, we can also assume that the animals traveled the second strech of their journey in the same time.

Dm = the distance the moose has traveled

Dr = the distance the rabbit has traveled

T = the time to destination

The moose traveled the first leg of its journey (Dm) in four hours and five minutes (4:05) where as the rabbit travled his distance (Dr) in two hours and five minutes (2:05). We also know that the second leg of the mooses journey is the same distance as the rabbits (Dr) and that the second half of the rabbits journey was the same distance as the mooses journey (dm). With this information we can then establish two equations.

(Knowing that the speed is constant and the equation for speed is Speed = Distance / Time)

Dm / [4:05] = Dr / T (This represent the speed of the first leg equals the speed of the second leg)

Dr / [2:05] = Dm / T

There are three variables but only two equations, so we solve for T, simplifing first.

Dm * T = Dr * [4:05] and Dr * T = Dm * [2:05]

T = (Dr * [4:05]) / Dm

T = (Dm * [2:05]) / Dr

Now we set the equations equal to each other.

(Dr * [4:05]) / Dm = (Dm * [2:05]) / Dr -simplify

Dr * Dr * [4:05] = Dm * Dm * [2:05]

Dr^2 * [4:05] = Dm^2 * [2:05]

Dr^2 * 1.96 = Dm^2

Now, using the law that the square root of A*B equals the square root of A * the square root of B we get... (This does assume that all values here are positive.)

Dm = Dr * 1.4

Substituting Dm's value into the original equation gives us...

T = (Dr * [4:05]) / (Dr * 1.4)

T = [4:05] / 1.4

T = [2:55]

So, the time it takes the moose and rabbit to get from their meeting point to their destinations is two hours and fifty-five minutes. So, two hours and fifty-five minutes from five minutes past four o'clock would mean that the animals arrived at their respective destinations at exactly seven p.m. [7:00]

[bonanova]

August has it.

Let d be the total distance traveled

Let f be the fraction of the distance the moose traveled when they met.

Let v_m be the moose's speed and v_r be the rabbit's speed.

v_m = fd/245. Moose arrives [1-f]/[f/245] = 245[1-f]/f minutes after 4:05 = 245/f minutes after noon.

v_r = [1-f]/125. Rabbit arrives f/[(1-f)/125] = 125f/[1-f] minutes after 4:05

equating the arrival times and solving gives f = .58333333 ...

245/f = 420 minutes, which is 7:00pm

[Guest]

It is 19:00 hrs

[Guest]

Presumably I'm missing something obvious.

obviously it works if Moose County and Banishire are the same place. They both go for a walk on a "circular" route that takes them back to their starting point, and both finished at exactly 4.05pm.

But then they're more likely to meet in the pub after their walk, rather than on the road!

Sorry for this very late response. I forgot that I posted it. Moose County and Banishire are different places with a single road joining them on a straight line. There is no trick. Its a pretty straight forward question.

[Guest]

August717, bonanova, Ben Law, all of you got it right. Sorry for the late response.