Long Division(By hand)

Mariner · 2011-02-15 12:20:36

Hi all, I have a question to do with long division. My question is what do I do with the remainder?
For example:

Vehicle A and vehicle B are 2548 miles apart and move towards each other.
The speed of vehicle A is 264 mph and the speed of vehicle B is 324 mph.
Where (distance from the startpoint of vehicle A) will both vehicles meet?

V(a)=264
V(b)=324
D=2548

V(t)=264+324=588

T= D/S

2548/588

Now thats where I stuff up somewhere. I use long division and I get quotient of 4 with a remainder of 196; I know the answer is going to end up as 4...something and then I need to multiply that by 264 but I don't know how to figure what comes after the 4. Please help! I know it's very basic math but I am always getting stuck at this part.

Last edited by Mariner (2011-02-15 12:22:46)

John E. Franklin · 2011-02-15 12:32:37

Since rate times time is distance, it is a linear equation, a line, distance on vertical y-axis,
rate or time, you pick it is on the x-axis, horizontal to the right.
This straight line means you can do reciprocals!! I don't know why I
know this, but the answer must be:
Distance of A =[ 324 / ( 324 + 264) ] times 2548.
Don't ask me how I know this, I just do... I'm old, 45 + or - 5 years.
bye. lol.

Mariner · 2011-02-15 12:44:11

John E. Franklin wrote:

Since rate times time is distance, it is a linear equation, a line, distance on vertical y-axis,
rate or time, you pick it is on the x-axis, horizontal to the right.
This straight line means you can do reciprocals!! I don't know why I
know this, but the answer must be:
Distance of A =[ 324 / ( 324 + 264) ] times 2548.
Don't ask me how I know this, I just do... I'm old, 45 + or - 5 years.
bye. lol.

Hi Thanks for the input but it's still a little off. You working got 1404 or 145.46 I cant remember while the answer is 1144, so it's almost in the ball park.

Last edited by Mariner (2011-02-15 12:48:11)

John E. Franklin · 2011-02-15 13:27:59

Vehicle A is the slower one, so you have given the distance from B I think.
Add them up, and you get the total distance...

Mariner · 2011-02-15 13:29:59

John E. Franklin wrote:

Vehicle A is the slower one, so you have given the distance from B I think.
Add them up, and you get the total distance...

You assume Vehicle A is traveling towards B. I know how to do the question just not the long division part.

John E. Franklin · 2011-02-15 13:35:37

Oh, long division, sorry, the 196 goes over the 588.
So you get 4 and 196/588. Does that help?

Mariner · 2011-02-15 13:39:28

John E. Franklin wrote:

Oh, long division, sorry, the 196 goes over the 588.
So you get 4 and 196/588. Does that help?

yeah this is where I get stuck because to remainder is larger than the divisor so what am I meant to do to get 0.3

John E. Franklin · 2011-02-15 13:42:53

Oh, I see it now!!
196 times 3 is 588, so 1/3 = 0.3333333333333333 forever.
So the answer of the division is 4.3333333333 repeating.

Mariner · 2011-02-15 13:46:46

John E. Franklin wrote:

Oh, I see it now!!
196 times 3 is 588, so 1/3 = 0.3333333333333333 forever.
So the answer of the division is 4.3333333333 repeating.

yes its recurring. So once I do all the long division and I get like a 4. something and I have a reminder, I divide the remainder by the divisor and get my decimal point. very nice

John E. Franklin · 2011-02-15 13:47:22

If you want you can bring down the invisible zero and keep dividing.
So you get 1960 divided by 588, and then pick 3, and go
around and around getting the same answer again and again,
bringing down a zero.

Mariner · 2011-02-15 13:52:54

John E. Franklin wrote:

If you want you can bring down the invisible zero and keep dividing.
So you get 1960 divided by 588, and then pick 3, and go
around and around getting the same answer again and again,
bringing down a zero.

sure can!, but I'm trying to do the question in under or as close to 30 seconds as I can by hand.

John E. Franklin · 2011-02-15 13:55:32

Okay, sounds good. Speed is good sometimes.
So now are you going to find out how much time it took for them to meet?
And then take that time and multiply it by the slower A rate for the distance,
supposing they are approaching each other in opposite directions...??

John E. Franklin · 2011-02-15 13:57:54

oh my gosh, I just realized I originally did the distance from point B.
Sorry about that, I wasn't thinking correctly...
Yes the distance to point A would be shorter because it is slower car.

Mariner · 2011-02-15 14:00:45

John E. Franklin wrote:

Okay, sounds good. Speed is good sometimes.
So now are you going to find out how much time it took for them to meet?
And then take that time and multiply it by the slower A rate for the distance,
supposing they are approaching each other in opposite directions...??

pretty much. So it's 4.3 x 264 =1135.2 so 1135. We just assume aircraft or A is traveling towards B. We don't worry about which is faster or slower unless it says Where (distance from the startpoint of vehicle B) will both vehicles meet?

John E. Franklin · 2011-02-15 14:05:06

Right, so 1144 miles from point A, the shorter distance.
And 1404 miles from point B, seems to me.

Mariner · 2011-02-15 14:19:19

John E. Franklin wrote:

Right, so 1144 miles from point A, the shorter distance.
And 1404 miles from point B, seems to me.

well you only do it for the point or aircraft it asks for, and as it's recurring it's just 4.3 x A's speed = 1135

Last edited by Mariner (2011-02-15 14:19:42)

John E. Franklin · 2011-02-15 14:23:54

If you shorten the number 4.3 instead of 4.33333, then it is just a little less accurate.
No big deal.

Mariner · 2011-02-15 14:25:44

John E. Franklin wrote:

If you shorten the number 4.3 instead of 4.33333, then it is just a little less accurate.
No big deal.

well if you can do 4.3333333 x 264 and all the other stuff in under 30 seconds be my guest lol

John E. Franklin · 2011-02-15 14:28:27

Well, we could use my first formula fixed of errors:
Wrong way: A =[ 324 / ( 324 + 264) ] times 2548.
Right way: A = [264 / (324 + 264) ] times 2548.
Comes out 1144.

John E. Franklin · 2011-02-15 14:29:32

I guess calculators aren't allowed here, huh?

Mariner · 2011-02-15 14:29:53

John E. Franklin wrote:

Well, we could use my first formula fixed of errors:
Wrong way: A =[ 324 / ( 324 + 264) ] times 2548.
Right way: A = [264 / (324 + 264) ] times 2548.
Comes out 1144.

are you doing this my hand or by calculator

John E. Franklin · 2011-02-15 14:31:08

Well this very last one I cheated and used a calculator!!
But before I was doing it in my head.

Mariner · 2011-02-15 14:32:38

John E. Franklin wrote:

Well this very last one I cheated and used a calculator!!
But before I was doing it in my head.

well I'm practicing for an aptitude test where I have to do about 75 questions in 24 minutes. I am given a ball part with these kinds of questions to work with so I think the method I used is quite accurate.

John E. Franklin · 2011-02-15 14:33:33

Yes, I agree. The division by 588 worked really well, and then
multiplying by 264 was fast. Nice work!!!!

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#1 2011-02-15 12:20:36

Long Division(By hand)

#2 2011-02-15 12:32:37

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#3 2011-02-15 12:44:11

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#4 2011-02-15 13:27:59

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#15 2011-02-15 14:05:06

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