SOLUTION: A mason and his assistant work together for 4 hours on a brick fireplace before the mason has to leave the job. The assistant finishes the job alone in 10 hours. If the mason can c
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Question 914657: A mason and his assistant work together for 4 hours on a brick fireplace before the mason has to leave the job. The assistant finishes the job alone in 10 hours. If the mason can construct a fireplace in 12 hours working alone, how long does it take his assistant working alone to construct a fireplace?
I know this is a work problem and r*t=wc. If the problem was straight forward I would set it up as X/10 + x/12 =1 but how do i account for the fours hours already worked together?
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Work-problems like this are a type of Uniform Rates problem. Try this equational format: RT=J for rate, time, amount of job. The rates are in dimension of for 1 unit of time, usually.
Look at the rates for these workers.
Mason,
Assistant,
Mason+Assistant,
The sum of their individual rates is their rate when they work together. We do not yet know the time needed for the assistant to do this 1 job alone; but I am calling this time, x.
The arrangement of the time and the workers was to do 1 whole job. They work together 4 hours and then assistant works alone to finish in 10 hours.
The question essentially asks for finding the value of x.
See the way the equation uses the uniform rates rule!
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = the fraction of the job they get
done while working together
----------------------------
Let = time for assistant to finish
the job working alone
--------------------
(1)
--------------------
Equation for the assistant working alone:
(2)
--------------------
Multiply both sides of (1) by
(1)
(1)
---------------------
Multiply both sides of (2) by
(2)
(2)
(2)
(2)
---------------------
Set (1) = (2)
------------
The assistant working alone
takes 21 hrs
------------
check:
(1)
(1)
Multiply both sides by
(1)
(1)
That means:
-----------------
(2)
(2)
Multiply both sides by
(2)
OK
Hope I got it
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