Question

Together, Tim and Alan can unload a truck 6 in minutes. When Tim works alone, it takes him 9 minutes longer than Alan to unload the truck. How long does it take each person to unload the truck alone?

Answer 1

use the equation @hero provided earlier, in addition to the fact that tim takes 9 minutes longer than alan.

this will give you a system of equations to work with

Answer 2

Well, actually, you won't need to solve a system, but you will need to properly define variables.

Answer 3

yeah if you define tim's time in terms of alan's time (or vice versa), that would suffice

Answer 4

So to help you out, I will do most of the dirty work for you:

Let
T = the time it takes Tim to unload a truck alone
A = the time it takes Alan to unload a truck alone

Then the time it takes for them to unload a truck together is:

\[\frac{T \times A}{T + A} = 6\]

They give us that it takes Alan 9 minutes longer to unload the truck alone compared to the time it takes Tim so we can further define Alan's time as A = T + 9. We replace that in our formula to get:

\[\frac{T (T + 9)}{T + (T + 9)} = 6\]

If you do the math correctly, you will get the correct answer.

Answer 5

So 6's the answer right?:)

Answer 6

You have to find the values of T and A bro. If you read the question again, you will realize this.

Answer 7

sry. :) thanks for you help! :)

Answer 8

Do you have any clue how to solve it?

Answer 9

I get two solutions: t=-6 and t=9

Answer 10

Which of those solutions makes sense in the context of this problem ?

Answer 11

@dumbsearch2 :
That's one of the questions to answer. The other question is, "Can you show the work that you've done to get that result?".

Answer 12

I get -6 and 9? Which solutions should I put where? Look at the attached stuff:

Answer 13

I'm still looking for you to post your steps that show how you got those numbers. Also, only one of those numbers are correct; the other you have to discard since it doesn't make sense mathematically. Furthermore, you must realize you have only solved for T and still need to find A.

Answer 14

nope.... i still don't understand.... :( http://www.wolframalpha.com/input/?i=%28T%28T%2B9%29%29%2F%28T%2B%28T%2B9%29%29%3D6

Answer 15

you solved for Tim's time, T. now ask yourself which of the following makes sense:

Tim unloads a truck in -6 minutes (he finishes 6 minutes before he starts)
Tim unloads a truck in 9 minutes (he finishes 9 minutes after he starts)

Answer 16

keep in mind that math is a tool that models reality, but we have to keep an eye on the domain to make sure it corresponds with reality

Answer 17

The fact that you're using Wolframalpha to do the computation for you shows that there's a lot you don't know, yet need to understand.

Answer 18

:(

Answer 19

My approach to this problem will be different.

Answer 20

@saifoo.khan what would it be?

Answer 21

@saifoo.khan, it probably would, but trust me, even if you were to show the person your way, I doubt he would understand.

Answer 22

This same user had trouble computing this:

\[\frac{8 \times 56}{8 + 56}\]

Answer 23

O_O

Answer 24

And that's with a calculator

Answer 25

No disrespect towards you @dumbsearch2, but there's no need in hiding what you don't know.

Answer 26

I'm not trying to be harsh, I'm just stating the reality that exists for you.

Answer 27

So the formula you provided is a franction? what do i have to solve for? i'll try...

Answer 28

I solved a similar problem here:
http://openstudy.com/users/saifoo.khan#/updates/50fac4ffe4b022b322702102

Answer 29

The difference is "How long would it take them if they work together?" in this case it's "How long does it take each person to unload the truck alone?" so what would I change in the forumula or something?

Thank you so much. :( Sorry for my ignorance. Just ignore me if it gets out-of-hand. :(

Answer 30

You just have to go in reverse order of this problem to solve your's.

Answer 31

So I want to solve for T, which is time? How do I solve the fraction (what Hero provided, the folula). I tried doing the distribuate property on the top of the franction but no luck. :(

Answer 32

Yes. You have to solve for T.

Cross multiply. Get rid of : T+(T+9)

Answer 33

Actually, you should probably simplify T + (T + 9) before doing anything. Afterwards, you'll want to multiply both sides by the expression in the denominator.

Answer 34

don't see how i could

Answer 35

In order to simplify T + (T + 9), get rid of the parentheses. Then simplify T + T + 9
This will only work for the expression in the denominator. Don't worry about the expression in the numerator just yet.

Answer 36

I attempted to solve with the formula you provided, and I got to t^2 = 3t+54. What do I do from there, or is it incorrect? How should I go about solving this?

Answer 37

Here's the deal @dumbsearch2, when you post the work you have done, you need to post all of your steps, that way we can properly verify your steps because if you make a mistake, we can go over that particular step you are having trouble with. So when you post what you have done, post everything, not just the step you are currently stuck on. It is important that we see what you are stuck on in addition to how you got there to begin with.

Answer 38

So, I simplified the denominator, just as you said. So I had this:T(T+9)/2T+9=6.
Then, I multiplied the denominator on both sides. T(T+9)=6(2T+9).
I distributed.T(T+9)=12T+54
Then...Now here is the part I am not sure about...I distribute the T: T^2+9T=12T+54.
I moved the 9T to the right side: T^2=12T-9T+54.
So now I have this: T^2=3T+54
I am not sure what to do next. Thanks so much for you help!!!

Answer 39

Yes, that is correct. I guess I must have underestimated you because you have the correct steps thus far. At this point, you should recognize that what you need to do is place all terms on the left side to create a quadratic equation set equal to zero. Then solve the quadratic for T. Any time you solve a quadratic, you get two values. In this case, we only need one value for T, the other will need to be discarded as it is not relevant.

Answer 40

So I found 9 for Tim after solving the quadratic. But I am sort of confused about Alan. If I understand correctly, T=9+A. But if this is the case, then A is 0. Is this even possible? Thanks again for your help. :)

Answer 41

Together, Tim and Alan can unload a truck 6 in minutes:
\[\frac{T \times A}{T + A} = 6\]
When Tim works alone, it takes him 9 minutes longer than Alan to unload the truck:
T = A + 9 How long does it take each person to unload the truck alone? So what we have to do here is substitute the value of T into the working together equation:

\[\frac{(A + 9) \times A}{2A + 9} = 6
\\A^2 + 9A = 6(2A + 9)
\\A^2 + 9A = 12A + 54
\\A^2 - 3A - 54 = 0
\\A^2 - 9A + 6A - 54 = 0
\\A(A - 9) + 6(A - 9) = 0
\\(A - 9)(A + 6) = 0\]
A = 9 or A = -6

-6 makes no sense for this type of problem. A = 9 is the correct value here.

Now since Tim works 9 minutes longer, we have:
T = A + 9
T = 9 + 9
T = 18

Thus Tim works for 18 minutes alone.

Answer 42

Thank you so much! :))) For your time! :) It works!!!! :)

Answer 43

Your the best person EVER! :D

Answer 44

Sorry for the confusion bro. Now you see why it is important to correctly define variables.

Answer 45

Nope, now it's clear! I can't believe you helped me so much! :) Your so nice..

Answer 46

Well, actually, initially, I was trying to help, but I spent the remainder of the time making up for the mistake I made while trying to explain it. I never want to leave knowing that all I did was confuse a student even more. It would not sit right with me.

Answer 47

Well thanks ever so much: the answer worked! :) It's correct, and I understand how you did it. :)

Answer 48

Well, that's great. This should work for most if not all your working together problems.