Question

please please help ~ word problem for algebra 1
One printing machine works twice as fast as another. When both machines are used, they can print a magazine in 3 hrs. How many hours would each machine require to do the job alone?

thanks in advance xx

Answer 1

the equation is work rate x time = work done
and then work done by A + work done by B = total work done

i'm just kinda confused on how to go about setting it up ;3

Answer 2

Let's refer to the task of printing this magazine as '1 job.'

Let the rate at which one machine can do the job be \[\frac{ 1~job }{ x~hrs }~and ~the~other~rate~\frac{ 1~job }{2x~hrs }\]

Is this enuf info so that you can do the rest of the setup?

Answer 3

Find x, and then find 2x, Be certain to check your results.

Answer 4

so would it be...
\[\frac{ 2}{ 2x} + \frac{ 1 }{ 2x} = 1\]

Answer 5

you would add the rates of each
1/2x + 1/x
(the x is the unknown # of hours)
and then you would multiply by the time it takes the two of them to finish 1 job
(3 hours according to the problem)

so
\[ \left(\frac{1}{2x} + \frac{1}{x}\right)3 = 1 \]

Answer 6

your equation is almost correct, except you should multiply the left side by 3

Answer 7

ohh that makes sense :)
so using that equation... would the answer be 9?

Answer 8

there are 2 answers: 1 for each machine

Answer 9

i got 9 hours for the first machine and 18 for the second

Answer 10

\[ \left(\frac{1}{2x} + \frac{1}{x}\right)3 = 1 \\
\left(\frac{1}{2x} + \frac{2}{2x}\right)3 = 1\]

now add the two fractions on the left side. what do you get ?

Answer 11

\[\frac{ 3 }{ 2x} + \frac{ 6 }{ 2x} = 1\]
then 9/2x = 1
9 = 2x
so x = 9/2?

Answer 12

yes x= 4.5 hours (that is the fast machine)
the other machine takes twice as long: 2x= 9 hours

Answer 13

oh thank you so much ;3 i get it now