Question 971797
Trace carefully where all the given data fit.


RATES in JOBS per DAY
PERSON______________RATE
Peter_______________{{{1/8}}}
Sam_________________{{{1/10}}}
John________________{{{1/16}}}


Workers acting at the same time combine their rates through addition.
Sam and John together, 4 days.
Sam and Peter together, unknown t days.
ONE whole job is started and finished.


RT=J for relating rate, time, and quantity of job.


{{{highlight_green((1/10+1/16)*4+(1/10+1/8)t=1)}}}


{{{16*5}}}  is the lowest common denominator.  Multiply left and right sides of
the equation by this, and the denominators can be cleared; and then continue on
to solve for time in days,  t.