quadratic equation word problem

[B.P.]

A farmer intends to construct a windscreen by planting trees in a quarter mile row. His daughter points out that 44 fewer trees will be needed if they are planted 1 foot farther apart. If her dad takes her advice how many trees will be needed? A row starts and ends with a tree.(1 mile = 5280feet)

I'm pretty sure the answer is 221 (if I read the tiny words right) but I don't know how to get it and I don't know how to set up the problem to put it into the quadratic equation.

 

[stapel]

I'm pretty sure the answer is 221 (if I read the tiny words right) but I don't know how to get it

I'm sorry, but I don't know what this means...?

A farmer intends to construct a windscreen by planting trees in a quarter mile row. His daughter points out that 44 fewer trees will be needed if they are planted 1 foot farther apart. If her dad takes her advice how many trees will be needed? A row starts and ends with a tree.(1 mile = 5280feet)

What is the length, in feet, of a quarter mile? (Hint: Divide 5280 by 4.)

Suppose the trees are currently spaced "x" feet apart. Into how many "spaces" will the trees divide this quarter-mile distance? (Hint: Divide the distance by the spacing.)

If the spacing is increased by "1", what expression would represent the new spacing? (Hint: x + 1.)

What expression would then represent the new number of spaces? (Hint: Divide the distance by the new spacing.)

You are given that (the new number of spaces) is (the old number of spaces) less (forty-four). What equation represents this relationship?

Then solve the rational equation.

If you get stuck, please reply showing how far you have gotten. Thank you!

 

[Deleted member 4993]

A farmer intends to construct a windscreen by planting trees in a quarter mile row. His daughter points out that 44 fewer trees will be needed if they are planted 1 foot farther apart. If her dad takes her advice how many trees will be needed? A row starts and ends with a tree.(1 mile = 5280feet)

I'm pretty sure the answer is 221 (if I read the tiny words right) but I don't know how to get it and I don't know how to set up the problem to put it into the quadratic equation.

Start naming variables

how many trees will be needed = N...... If her dad takes her advice

How many feet apart will be the trees = 1340/(N-1)....... If her dad takes her advice

Now continue....(with what would happen if he didn't)

 

[B.P.]

I was referring to the answer key in my book for the part that wasn't understood in my earlier message (I should have been more specific)

For the problem, I came up with 1/4m = T and 1/4m + 1foot = T - 44 and I divided
5280/4 which equals 1320 so where does this go in the equation?

 

[Denis]

For the problem, I came up with 1/4m = T and 1/4m + 1foot = T - 44 ...

BeeP, did you at least READ what Subhotosh and Stapel told you?

Make up a SIMPLER case:
A farmer intends to construct a windscreen by planting trees in a 60 feet row.
His daughter points out that 2 fewer trees will be needed if they are planted 5 feet farther apart.
If her dad takes her advice how many trees will be needed?

This is the solution:

1 (10) 2 (10) 3 (10) 4 (10) 5 (10) 6 (10) 7       :     1 (15) 2 (15) 3 (15) 4 (15) 5

So we have m=10 and t=7; so m(t - 1) = 10(7 - 1) = 10(6) = 60
For other case: (m + 5)(t - 3) = 15(7 - 3) = 15(4) = 60
See that?

So the 2 equations are: m(t - 1) = 60 and (m + 5)(t - 3) = 60
The quadratic to be worked out from those.

Your problem will work out similarly: m(t - 1) = 1320 and (m + 1)(t - 45) = 1320
If you can't work that out, then you need classroom help.