Question

One machine can complete a production run at a factory in 46 hours. Two machines can complete the production run in 25 hours if they work together. How long would it take the second machine to complete the production run if it had to do the job by itself?

I think I have the answer to this, but I'd like to get a second opinion on what the answer is and how to calculate it.

Answer 1

hi,
for the first machine...
the rate of doing work is..
if the amount of work is "x"
the machine will complete x/46 amount of work per hour..

for the second machine..
if the second machine take "y" hours to complete the work "x"
the rate of doing work is...
the machine will complete x/y amount of work per hour...

if the 2 machines work together amount of work completed in a hour is...\[\frac{ x }{ y } +\frac{ x }{46 } = \frac{ 46x +x y }{ 46y }\]
and the questions says that the time take by those 2 machines together is 25...
so if we multiply the amount of work the 2 machines do in a hour by 25 we will get the total amount of work...

which is..
\[\frac{ x(46 + y) }{46y } \times 25 = x\]\[25(46 + y ) = 46y\]
\[21y = 25 \times 46\]\[y = \frac{ 25 \times 46 }{ 21 }\]
\[y = 54.76 \ hours\\]

hope this will help ya!!!

Answer 2

I used a different method to calculate it, but I got the same answer, so I'm happy with it :) Thanks for the help!

Answer 3

u r welcome !!

Answer 4

x = hours machine one can complete alone
y = hours machine two can complete alone
t = hours it takes if both work together

\[\frac{xy}{x + y} = t\]\[\frac{46y}{46 + y} = 25\]\[46y = 25(46 + y)\]\[46y = 1150 + 25y\]\[(46 - 25)y = 1150\]\[21y = 1150\]\[y = \frac{1150}{21}\]\[y = 54.76\]