A teacher gave me this for extra credit and i could not get it right when i was in school can you answer it ?

Question

A math teacher on vacation was driving along a country road to visit an ancient castle when she noticed that the passing trees had been planted an equal distance apart. So she glanced down at her clock when the car was midway between trees and counted the number that she passed in a minute. " How interesting!" she said to herself afterward. " When i multiply the number of trees by 10, the result equals the speed of my car in miles per hour." Assuming that the speed of the car was constant and that the minute ended midway between trees, how far apart were they?

Answer 1

This is relatively easy.

The teacher is travelling along the road, trees equidistantly spaced along the side.

She notices that the number of trees she passes is equal to 1/10 the speed of her car. Thus, if she's travelling 60 mph, she passes 6 trees; at 50 mph she passes 5 trees, etc.

60 mph = 88 feet/second (do the conversion!), and thus in one minute at 60 mph, she travels 60 x 88 feet = 5280 feet (= 1 mile)

6 trees in 5280 feet means there are 6 "segments" that she has traversed, so there are 5280/6 = 880 feet between trees.

Answer 2

she counted x trees in 1 min. = 60x trees/hour
She is travelling at 10x miles/hour

we can equate these 2 amounts.We can then see that 6 trees = 1 mile. We can then divide by 6 to get the distance between trees:

1/6 mile or 880 feet. Speed here does not matter.

Checking: to make things easy, she goes at speeds of 60 mph and 120 mph.

At 60 mph, she is traveling at 1 mile per minute. this woud convert to 6 trees. if we multiply this by 10, we get 60 trees, which is numerically equal to the speed.

At 120 mph, this converts to 2 miles per minute, or 12 trees.
12 * 10= 120 (what the matematician does in the question). Again numerically equal.

I hope you like this.... :)

Answer 3

At 60 miles per hour she would have passed 6 trees in a minute.
She also would have gone 1 mile, so the trees are 1/6 of a mile apart.

Answer 4

x= number of trees
t= 1 minute or 1/60 hour
f= distance between trees in miles
s=speed in miles per hour

10*x*f/t = s or f = s/(10*x)*t

entering the value for t and simplifying; f = 6*s/x

if we assume that she meant the NUMERICAL value of 10*x = s, then f = 6 * 10 * x/x or f = 60 feet.

Really I think this is a contrived way to word the question.

Hmm, I think we are missing something, either the number of trees or speed of the car.

Answer 5

I made a diagram (on paint, lol).
http://img319.imageshack.us/img319/4733/prob1rr8.jpg

Now: Check that:
x = distance between each tree
Z = total distance that the teacher drove during that minute
n = number of trees
v = speed of the car

Now,

nx = Z
x = Z/n

That means, n trees times the distance between each tree, will give you the total distance. We're cool, right?

So, v = total-distance/time = Z/t ; but we gotta check the dimensions, so:

v = Z/t = Z/1minute = Z(miles/minute)

Here comes the game: you got Z, n and x as variables you dont know, but they give you this info:

10n = v (miles/hour)

The thing is, they aren't using a real dimensional analysis, it's just a numerical relation, so we won't mind at all about the dimensions of both sides, but we do about the dimensions of v, because we now compare it... check it out:

if v = Z (i was careful converting them to the same dimensions, mile/minutes)

10n = v(miles/hour) = Z(miles/minute)(60minutes/hour)
10n = 60Z(miles/hour)
n = 60Z/10 = 6Z
Z = n/6

We continue with the first equation we obtained:

x = Z/n

And now we sustitute the value of Z

x = n/6n = 1/6 of mile = 0.1667 miles

Answer 6

Let t = number of trees passed.
10t = speed in miles per hour.
5280 × 10t / 60 = 880t = speed in feet per minute.

(Rate) × (Time) = (Distance)
(880t ft/min) × (1 min) = 880t feet.

The distance between the trees is the distance travelled divided by the number of trees.

D = 880t / t = 880 feet.

Answer 7

is that this the only thank you to get the greater credit? till you are able to gown as a result to 3 different public place or journey then it feels like a clean violation of the separation of church and state. in case you're tender with it, communicate over with the instructor. If no longer then take it to the vital. (in spite of in case you're tender with that or no longer.) in the event that they do no longer something then take it on up the chain of authority. If that is going nowhere then you somewhat can touch the ACLU. yet flow some way up the chain in the previous invoking the ACLU. that's a confrontational step and could positioned you in a spotlight (look on the flak from the present Rhode Island case). provide them a huge gamble to handle this privately and quietly.

Answer 8

5250 (a mile) / 6 (60mph/10=6 trees) = 875 ft between trees

Answer 9

There has to be more information. Like how many trees or how long a time period passed.

Answer 10

missing information