<PRE><B>Question 206831</B>
: 
three old machines together required 80 min to do a certain job.
 two new machines were installed one of which worked 3 times as fast as all the old machines put together.
 the five machines working together, took 15 min to do the same type of job.
 how long would it take the other new machine working alone to do the work?
:
Let t = time required for the other new machine to do the job
:
the three old machines (treated as a single unit) = 80; to do the job
:
One new machine time = {{{80/3}}} min; (3 times faster than the 3 old ones)
:
Let the completed job = 1
:
All 5 machines working together:
:
{{{15/t}}} + {{{15/(80/3)}}} + {{{15/80}}} = 1
Simplify the middle fraction to a decimal value:
{{{15/t}}} + .5625 + {{{15/80}}} = 1
Multiply equation by 80t, results:
80(15) + 80t(.5625) + 15t = 80t
:
1200 + 45t + 15t = 80t
:
1200 = 80t - 60t
:
1200 = 20t
t = {{{1200/20}}}
t = 60 min required by the other new machine alone
:
:
Check solution:
15/60 + 15/26.67 + 15/80
.25 + .5625 + 1875 = 1


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