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