Question

A wagon train that is one mile long advances one mile at a constant rate. During the same time period, the wagon master rides his horse at a constant rate from the front of the wagon train to the rear, and then back to the front. How far did that wagon master ride?

My teacher hates me its 10 extra credit points...anyone?

Answer 1

a constant rate but you do not know the constant rate?

Answer 2

nope

Answer 3

well the trick answer is two miles, since the train is one mile long and the "wagon master" rode from the front to the back and then to the front
but i am not sure if this is the answer you need

Answer 4

oh i see nvm that is wrong

Answer 5

lol i don't get it either

Answer 6

we can do this, give me a minute

Answer 7

lol ok

Answer 8

ok give me another few minutes

Answer 9

lol its takin me forever

Answer 10

think i am almost there

Answer 11

i think its impossible

Answer 12

no no less than a minute now

Answer 13

got it

Answer 14

let me know when you are ready, i will write a solution

Answer 15

first of all since it makes no difference apparently how fast the train goes, lets make it easy and make it go one mile per hour, so it completes its journey in one hour

Answer 16

ok

Answer 17

and what we are going to solve for is the rate of the horse, because if we know the rate of the horse we know the total distance. they will be the same since the total time will be one hour

Answer 18

i put the rate of the horse as \(x\)
and the rate of the train is 1, so as the horse travels to the rear of the train, the combined rate is \(1+x\) right?

Answer 19

yes

Answer 20

ok the horse travels one mile to the rear of the train at a speed of \(1+x\)
the time taken to reach the end of the train is distance divided by rate, so it takes
\[\frac{1}{1+x}\] to reach the back

Answer 21

now the horse turns around and heads to the front of the train. since it is going with the train the combined rate is now \(x-1\) and it has to complete its one mile journey at then end of one hour
it has already used up \(\frac{1}{1+x}\) hours leaving
\[1-\frac{1}{x+1}\] hours to go the one mile

Answer 22

using distance equals rate times time, we get
\[1=(x-1)(1-\frac{1}{x+1})\]

Answer 23

let me know if you are still with me, because this is really the end. just a matter of solving this equation

Answer 24

@satellite73 , I got x=3, I think that is the speed of the horse ?? 3 mph

Answer 25

i got \(1+\sqrt{2}\)
this took me quite a while
then i googled and got an answer i didn't understand, but it was still \(1+\sqrt{2}\)

Answer 26

i mean i didn't understand the method used to solve the problem. i am sure it was fine, but i did something else

Answer 27

O.K I am sure the speed of the wagon master was the same as the horse, that is about all that I am sure of. lol

Answer 28

truth be told i wolframed to solve the equation.
i guess i should do it with pencil and paper

Answer 29

lol i got 3 too, but we both must have made the same mistake!

Answer 30

http://www.wolframalpha.com/input/?i=1%3D%28x-1%29%281-%281%2F%28x%2B1%29%29%29

Answer 31

algebra challenged today

Answer 32

Well I worked it differently and got \[1\pm \sqrt{2}\] I think I will go get a cup of coffee, Have a nice day satellite73.

Answer 33

Just checked your link, I got close lol

Answer 34

second time i got
\[1=x-1-\frac{x-1}{x+1}\]
\[\frac{x-1}{x+1}=x-2\]
\[x^2-2x-1=0\] so now i am happy
yes, it is coffee time
have a good one