# word problem

#### ptebwwong

##### New member
Can someone tell me how to setup this problem?

A new copy machine works three times faster than the older model. It takes 12 minutes to complete a job when both machines are working together. Find the time required for the new copy machine to complete the job by itself.

#### galactus

##### Super Moderator
Staff member
If we let t=the time it takes for the old machine to do a job alone, then it can do 1/t part of the job in one minute.

The new machine is 3 times as fast, so we have 3/t.

$$\displaystyle \frac{1}{t}+\frac{3}{t}=\frac{1}{12}$$

Solve for t.

You can do the other problem in a similar manner.

#### Loren

##### Senior Member
The key is to recognize what is accomplished in one unit of time, in this case, in one minute. In setting up your equation, be sure to name things. You will want to investigate "the number of minutes to do the job", and "how much of the job can be done in one minute".

Let time it takes for new machine to do the job alone be called x minutes.
Then time it takes for old machine to do the job alone is 3x minutes.
The time it takes for them working together is 12 minutes.

In one minute new machine can do 1/x of the job.
In one minute old machine can do ____ of the job.
In one minute working together they can do ____ of the job.

Now, write your equation on basis that in one minute the amount of job new machine does added to the amount of job the old machine does equals the amount of the job done by their working together.

#### Loren

##### Senior Member
I see that galctus and I doubled. Note that I named my variable in terms of the new machine because I wanted my variable to be that which was asked for. Galactus named his variable in terms of the old machine. You solve his equation to get t, but the problem asks for 3t, so you have to be aware of that.

#### foothillstudent_12

##### New member
hi My name is De Shaun and i am new to this website but i think i can help you, now mind you i am not a genius so it might not be right but it's worth a try

1/t+3/t=1/12
=4/t=1/12
4/t x 4=t
1/12 x 4 = 4 4/12
t=4 4/12

but i advise someone look over my answer so you wont get it wrong i hope i was some kind of help

#### chivox

##### Junior Member
foothillstudent_12 said:
hi My name is De Shaun and i am new to this website but i think i can help you, now mind you i am not a genius so it might not be right but it's worth a try

1/t+3/t=1/12
=4/t=1/12 >>> Or, just cross multiply here... 48 = 1t
4/t x 4=t >>> (4/t) (t) would equal 4, but (4/t)(4) = 16/t
1/12 x 4 = 4 4/12 >>> Actually it equals 4/12, without the whole number, but that's beside the point.
t=4 4/12

but i advise someone look over my answer
There are some errors in your arithmetic (you really have to be more careful, foothill), but also I want you to think logically about what this answer means. If both machines complete the task in 12 minutes when they're both working on the task together, how could just the one machine (the old one at that) complete it in under 5 minutes?

Once you get the answer, take a step back and figure out if it makes any sense. If it doesn't make sense in the context of the problem, something's wrong. In your case, there are too many "4"s floating around in your arithmetic. But that problem can be fixed. As for the logic flaw, you just have to remember that you're working on real problems here, not just manipulating some numbers.

#### foothillstudent_12

##### New member
i understand what you are telling me and now that i look at the problem again you are correct that is why i advised the person who is doing the problem to get it overlooked again because i was unsure but thanks for the advice i actually signed on here because i am having problems in math at the moment with the grade of a D-. So i need all the help i can get