Distance Apart

[Guest]

A passenger on a train observes that 4.5 times the number of spaces between utility poles that are passed in a minute is the rate of the train in mph. Determine distance the poles are apart.

Answer with problem: 198 ft.

How do I solve?

[Guest]

This is an algebra question.
As usual let some symbol/letter represent the quantity you have to find. In this case the space between poles.
So let S = space in feet.
Make up equations relating the poles, spaces and the speed from the info in the question
Then solve the equations.

[Guest]

S = space in feet.

1 space between 2 poles.

4.5 x 1 = 4.5

4.5 x 60 sec . per min = 270

Not sure.

[Guest]

S = space in feet. ........OK

1 space between 2 poles ....OK ....yes there will only be 1 space between 2 poles...probably irrelevant to know this..???

Don't know your thinking for the rest of you calculations..??? what were you trying to calculate..?????


You need to make good use of this information given in the question......
......... 4.5 times the number of spaces
....................passed in a minute
............................rate of the train in mph

and note we are measuring the space distance in feet, and the train speed is in mph.

[Guest]

" what were you trying to calculate..????? " 4.5 times the number of spaces between utility poles that are passed in a minute.

88 feet per minute = 1 mile per hour.

I still don't know.

[Guest]

Your next step needs to be sorting out this information so that you understand the question.
...........................
You need to make good use of this information given in the question......
......... 4.5 times the number of spaces
....................passed in a minute
............................rate of the train in mph

and note we are measuring the space distance in feet, and the train speed is in mph.
.....................................

88 feet per minute = 1 mile per hour......Yes it is good to know this but not much help right now.

it would be helpful if we could quantify the number of spaces passed each minute.......we could let it equal N for now.

Then the number of spaces passed per minute multiplied by the distance of each space in feet would give us the number of feet per minute. we can express it in terms of the symbols we have already defined. Then we can define the distance travelled each hour in feet and also in miles and we are told this equals 4.5 times the number of spaces passed

[Guest]

S = speed

4.5N = S

I don't know.

[Guest]

In earlier post we stated we would let S = space between poles in feet.

Now you are wanting S = speed .....why???? .... and you have not indicated any units, is it feet per minute or miles per hour ???

and you state 4.5N = S the question say 4.5N is equal to the speed in miles per hour. You will have to apply some of the facts and figures given in the question to get this solved, and remember the question asks you to find the length of the space between poles.

Follow the pointers I gave in my last few posts to build the equations necessary to solve.

[Guest]

S = space in feet.

Sorry for error.

[Guest]

OK, but you are not attempting to do the question.

put some expressions down relating to the info given in the question

[Guest]

if as you say S was meant to be feet, then why did you say 4.5N = S.......what you seem to be saying here is ..... 4.5 x N (number of poles) = Space between each pole......surely this must be wrong

[Guest]

4.5 times the number of spaces passed in a minute = rate of the train in mph.

S = spaces in feet.
N = number of spaces.

60N = number of spaces in minute.

4.5 x 60N = rate of train (mph).

I don't how to solve.

[Guest]

4.5 times the number of spaces passed in a minute = rate of the train in mph. ......yes

so we said N was the number of spaces passed per minute and S was the length in feet of each space, so N x S is the length in feet travelled per minute
but the rate of the train is in miles per hour and if we know the length travelled per minute we can find the length travelled per hour and if we know the length travelled per hour we can say it is equal to 4.5 times the number of spaces passed per minute

[Guest]

" so we said N was the number of spaces passed per minute and S was the length in feet of each space, so N x S is the length in feet travelled per minute
but the rate of the train is in miles per hour and if we know the length travelled per minute we can find the length travelled per hour and if we know the length travelled per hour we can say it is equal to 4.5 times the number of spaces passed per minute "

I still don't know.

[Guest]

88 feet per minute = 1 mile per hour.
You are not even making use of this and you posted it yourself earlier.....
This comes about from the fact there are 5280 feet in a mile and 60 minutes in an hour

So 1 mile per hour OR 5280 feet per hour = 5280 / 60 = 88 feet per minute.

In the question S is the space in feet and N is the number of spaces per minute
So N x S normally written as NS is the number of feet per minute and from above we know that every 88 feet per minute corresponds to 1 mile per hour

So if I divide by 88 I will get the mph........So......NS/88 mph

and the question states this is equal to 4.5 times the number of spaces passed per minute ...So.....NS/88 = 4.5N
The "N" cancels from each side of the equation to leave ..... S/88 = 4.5 ....so.... S = 4.5 x 88 = 396 feet per space

and this is twice your suggested answer......?????....but I think I am correct except someone can logically tell me I am wrong....

[Guest]

Thanks again.


" 88 feet per minute = 1 mile per hour.
You are not even making use of this and you posted it yourself earlier..... " As I didn't know how to solve, I did not know where in the solution it was used.

" and this is twice your suggested answer......?????.... " The 198 was provided with problem. I have no idea how they arrived at that.