# Math Help - Story Problems

1. ## Story Problems

I seem to get a better response at 3am for some reason...... or my last post is invisible.
I dont know. Anyway.

I would DEEPLY appreciate a quick response on these, as the final is in 12 hours.. and i still a lot to do.... been working on it for 3 days strait.. and was even up till 5:30 am last night doing it. Its that friggin hard. but ill never have to do it again after this (and more than likely ill never be back....)

//remember// i have the answers.. i dont need the answers, i need to know HOW to get the answers.

32. The length of a rectangle is 10 more than the width. the area is 96 square inches. Find the dimentions.

I think it'd be w(w+10)=96. But that doesnt work out. (the answer i get is width=8", length=18")

33. Find 2 consecutive positive integers whose product is 420.

I think it'd be n+n+2=420. but again, it doenst work out. it turns out to be some 1/2 number.

36. You inherit 5000$, which you decide to invest. You invest part of the money at 4% interest and part of the money at 6.5% interest. After one year you earn$285 in interest. How much did you invest at each rate?

answer: $1600 invested at 4%,$3400 invested at 6.5%

37. Two planes leave an airport at approx. the same time and fly in opposite directions. Their speeds are 510mph and 600mph. How far apart will they be after 1.5 hours?

In the event someone responds to these and they get answered, i have 38-43 left.. They involve functions.... graphing.. slopes..

But im guna work on these by myself for a few hours first..

2. Originally Posted by Cait
32. The length of a rectangle is 10 more than the width. the area is 96 square inches. Find the dimentions.

I think it'd be w(w+10)=96. But that doesnt work out. (the answer i get is width=8", length=18")
Call the width of the rectangle w. Then the length is (w + 10).

So
A = w(w + 10) = 96

w^2 + 10w - 96 = 0

(w - 6)(w + 16) = 0

w = 6 or w = -16

We discard the -16 as unphysical, so w = 6 and l = 16.

-Dan

3. Originally Posted by Cait
33. Find 2 consecutive positive integers whose product is 420.

I think it'd be n+n+2=420. but again, it doenst work out. it turns out to be some 1/2 number.
Call the first integer n. Then the second integer is n + 1. So the product of them is:
n(n + 1) = 420

n^2 + n - 420 = 0

So n = 20 or n = -21

Since the integers must be positive (according to the problem statement) n = 20 and n + 1 = 21.

-Dan

4. Originally Posted by Cait
37. Two planes leave an airport at approx. the same time and fly in opposite directions. Their speeds are 510mph and 600mph. How far apart will they be after 1.5 hours?

d = vt
where d is the distance travelled, v is the speed, and t is the time.

So the first plane flies:
d = (510 mi/h)(1.5 h) = 765 mi

The second plane flies
d = (600 mi/h)(1.5 h) = 900 mi

Since the planes are flying in opposite directions then we simply add the two distances:
765 mi + 900 mi = 1665 mi

-Dan

5. Ohh 3 of them!! thanks so much!! ))

(btw: I got to go to Fermilab, where they make top quarks! super cool! )

6. Originally Posted by Cait
Ohh 3 of them!! thanks so much!! ))

(btw: I got to go to Fermilab, where they make top quarks! super cool! )
I didn't know Fermilab was big enough to make top quarks. Cool.

But for the record my user name is "top squark." A squark is the supersymmetric spin 1 particle paired with a quark. No one knows if such a thing exists yet. (And it was a username on Yahoo that hadn't been taken yet. All the quarks were already in use. )

-Dan