Mixing Word Problems & Distance Word Problems

demha · 2012-12-26 00:01:53

Hi guys, I was just wondering if I got these correct. The ones that have the answers in bold letter is the one I need help with (ones I haven't answered correctly).

1.
Q. A container is partially filled with 12 liters of whole milk containing 4% butterfat. How much 1% milk must be added to get a mixture that is 2% butterfat? Construct a table, then solve.

A.
   Amount of milk Percentage(%) Amount of buttermilk
1%    x    (0.01)    (0.01)x
4%    12    (0.04)    (0.04)x
2%    x + 12    (0.02)    (0.02)(x + 12)

Let milk = m
(0.004) x (12) = (0.48) liters of fat

(0.01) x m = (0.01)m

2 + m

(0.48) + (0.01)m

0.48 + (0.01)m = (0.02) x (12 + m)

0.48 + (0.01)m = 0.24 x (0.02)m

0.24 = (0.01)m

m = 24 (you will need 24 liters)

3.
Q. An 80-pound grass seed mixture is 30% bluegrass seed. How many pounds of seed containing no bluegrass seed (0%) should be added to the seed mixture for a resulting blend that is 20% bluegrass seed? Construct a table, then solve.

A.
How would I set a table for this?

4.
Q. A boat travels 60 km upstream (against the current) in 5 hours. The boat travels the same distance downstream in 3 hours. What is the rate of the boat in still water?

A. The rate is 4 current.

5.
Q. A duck can fly 2400 m in 10 minutes with the wind. Against the wind, it can fly only 2/3 of this distance in 10 minutes. What is the rate of the wind?

A.
How would I do this?

demha · 2012-12-26 00:03:00

For #1, the first thing you see is a supposed table. I need help creating a table for number 2. For number 5 I am not too sure how to do, the rest I'm just wondering if I did them correctly.

bobbym · 2012-12-26 00:13:03

Hi;

For #5)

I am getting

velocity of the duck = 200 m / minute and the velocity of the wind is 40 m/ minute.

scientia · 2012-12-26 00:37:37

demha wrote:

4.
Q. A boat travels 60 km upstream (against the current) in 5 hours. The boat travels the same distance downstream in 3 hours. What is the rate of the boat in still water?
A. The rate is 4 current.

Let b be the velocity of the boat in still water and c be the speed of the current. Then you have

Solve the two simultaneous equations for b.

demha wrote:

5.
Q. A duck can fly 2400 m in 10 minutes with the wind. Against the wind, it can fly only 2/3 of this distance in 10 minutes. What is the rate of the wind?
A.
How would I do this?

As above you must set up two simultaneous equations and solve them. Let d be the velocity of the duck in still air and w the speed of the wind. The first equation is

I leave you to derive the second equation and solve the them for w.

Last edited by scientia (2012-12-26 00:40:18)

Bob · 2012-12-26 00:53:33

hi demha

I got a bit confused by your working for Q1 but I agree with the answer you got.

Q3. My table below. The two bluegrass weights must be equal.

Bob

demha · 2012-12-26 02:30:03

Hi Bobby:
So it would be 40m/a minute?

Hi Scientina:
I'm not too sure how t continue. Could you please help me a little on that?

Hi Bob:
Now how would I create tat chart? I was also wondering, did I do that chart correctly?

Last edited by demha (2012-12-26 02:30:44)

bobbym · 2012-12-26 03:09:19

hi demha;

Yes, I am getting 40 meters per minute for the windspeed.

Bob · 2012-12-26 03:49:59

hi

I was also wondering, did I do that chart correctly?

Do you mean this one:

A.
Amount of milk Percentage(%) Amount of buttermilk
1% x (0.01) (0.01)x
4% 12 (0.04) (0.04)12
2% x + 12 (0.02) (0.02)(x + 12)

There's a little error which I have corrected in red.

What I did is say that the first and second row figures for buttermilk must add up to the last row.

multiply by 100 to remove the decimals

Now how would I create tat chart?

In a word problem, I was taught to find out what I must calculate and call that x.

Then summarise all those words in a table with just the essential details.

There is the start mix, the added seeds and the final mix so the table will need three rows after the headings.

And there are three seed types to consider, mix, bluegrass alone, other seeds alone, so that makes three columns.

Rather than putting in % I converted everything into weights in lb. That keeps it simple.

Row one plus row two must make row three.

I didn't bother with the final entry as it isn't needed to get x. But you might like to try to complete it for the practice. You can solve for x using column three as well. try it.
Bob

demha · 2012-12-26 04:47:15

Hi Bob:
Yes that's the one! I found that mistake soon after too. I remember adding that 12 there, I wonder how an x replaced it? o_O

As for the second chart, this is what I did:
Seed Weight Blue Grass Weight Other Seed
0%    x 0.00    (0.00)(x)
30% 80 0.30    (0.30)(80)
20% x + 80 0.20    (0.20)(x + 80)

Bob · 2012-12-26 05:58:56

hi demha

Not quite.

Seed Weight Blue Grass Weight Other Seed
0% x√ 0.00√ (0.00)(x)X(i)
30% 80√ 0.30X(ii) (0.30)(80)X(iii)
20% x + 80√ 0.20X(iv) (0.20)(x + 80)X(v)

(i) This is the weight of the other seed. If x lb is added and all is other seed what should go here?

(ii) Work out 30% of 80 and write the answer here.

(iii) Work out 70% of 80 and write the answer here.

(iv) (x + 80) is correct for the first number in this row. Write an expression for 20% of (x + 80) here.

(v) And an expression for 80% of (x + 80) here.

Bob

demha · 2012-12-26 17:34:44

Seed Weight Blue Grass Weight Other Seed
0%    x 0.00    (x)(just x will go here I believe)
30% 80 24    (0.30)(56)
20% x + 80 16    (0.20)(x + 64)

So is this right then?

scientia · 2012-12-26 18:26:41

demha wrote:

Hi Scientina:
I'm not too sure how t continue. Could you please help me a little on that?

What are you not too sure of? The two problems are similar, and I did almost all of question 4 for you. Just apply the concept speed = distance / time.

demha · 2012-12-26 20:01:09

Hi Scientine:
I was taught how to do it using d = rt but wasn't understanding it right.

Now for what you shows me, am I supposed to substitute C for the current (which I got as 4) and then continue to solve for B?

Last edited by demha (2012-12-26 20:06:45)

Bob · 2012-12-26 20:52:16

hi demha

Seed Weight Blue Grass Weight Other Seed
0% x 0.00 (x)(just x will go here I believe)√
30% 80 24 (0.30)(56)X just 56 here
20% x + 80 16X(i) (0.20)(x + 64)X(ii)

(i)The total amount in this row is x + 80. 20% of it should go here so put 0.2(x+80)

(i)And a similar expression here but this time for 80% of (x+80)

Now you are ready to solve the puzzle.

You can do the blue grass equation: 0 + 24 = 0.2(x+80)

or the other seed equation x + 56 = 0.8(x+80)

These should both give the same answer for x.

Check it works with the original problem.

Q4 and Q5. I have put the details for both of these into a table as well. (See below)

These three formulas are equivalent:

The answer will be in metres per minute.

Bob

scientia · 2012-12-26 21:30:49

demha wrote:

Hi Scientine:
I was taught how to do it using d = rt but wasn't understanding it right.
Now for what you shows me, am I supposed to substitute C for the current (which I got as 4) and then continue to solve for B?

Yes, you need to solve for b because the question is asking for the boat's speed in still water: in other words, what boat's speed would be if there were no current at all. The question isn't asking for the speed of the current (so your answer was not correct).

Bob bundy has created two tables for you for these two questions. Have a look. I think you might understand the questions better from the tables.

demha · 2012-12-26 21:44:35

Hi Bob:
I redid it again:

Seed Weight Blue Grass Weight Other Seed
0%    x 0.00    (x)(just x will go here I believe)
30% 80 24    (56)
20% x + 80 0.2(x+80)    (0.8)(x + 80)

demha · 2012-12-26 21:52:51

5 = 60/(x - 4)
x - 4 = 60/5
x - 4 = 12 (add 4 to both sides)
x = 16

So the rate will be 16 kilometers an hour in still water.
Am I heading the right direction?

demha · 2012-12-26 21:56:41

Hi Bob:
With your equation, I did the math and gor x = 40, so it will take 40 pounds of no-blue-grass seeds. Am I correct?

Bob · 2012-12-26 22:12:29

hi demha

Well done. Both answers, 16 and 40, are correct!

Bob

demha · 2012-12-29 21:28:06

Thank you very much guys! I got a 10 on my final review!!

bobbym · 2012-12-30 15:05:09

Hi;

That is very good! I see you had a lot of good help.

Math Is Fun Forum

#1 2012-12-26 00:01:53

Mixing Word Problems & Distance Word Problems

#2 2012-12-26 00:03:00

Re: Mixing Word Problems & Distance Word Problems

#3 2012-12-26 00:13:03

Re: Mixing Word Problems & Distance Word Problems

#4 2012-12-26 00:37:37

Re: Mixing Word Problems & Distance Word Problems

#5 2012-12-26 00:53:33

Re: Mixing Word Problems & Distance Word Problems

#6 2012-12-26 02:30:03

Re: Mixing Word Problems & Distance Word Problems

#7 2012-12-26 03:09:19

Re: Mixing Word Problems & Distance Word Problems

#8 2012-12-26 03:49:59

Re: Mixing Word Problems & Distance Word Problems

#9 2012-12-26 04:47:15

Re: Mixing Word Problems & Distance Word Problems

#10 2012-12-26 05:58:56

Re: Mixing Word Problems & Distance Word Problems

#11 2012-12-26 17:34:44

Re: Mixing Word Problems & Distance Word Problems

#12 2012-12-26 18:26:41

Re: Mixing Word Problems & Distance Word Problems

#13 2012-12-26 20:01:09

Re: Mixing Word Problems & Distance Word Problems

#14 2012-12-26 20:52:16

Re: Mixing Word Problems & Distance Word Problems

#15 2012-12-26 21:30:49

Re: Mixing Word Problems & Distance Word Problems

#16 2012-12-26 21:44:35

Re: Mixing Word Problems & Distance Word Problems

#17 2012-12-26 21:52:51

Re: Mixing Word Problems & Distance Word Problems

#18 2012-12-26 21:56:41

Re: Mixing Word Problems & Distance Word Problems

#19 2012-12-26 22:12:29

Re: Mixing Word Problems & Distance Word Problems

#20 2012-12-29 21:28:06

Re: Mixing Word Problems & Distance Word Problems

#21 2012-12-30 15:05:09

Re: Mixing Word Problems & Distance Word Problems

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