Question 81772
An executive secretary can finish a typing job in 10 hours while an
ordinary employee can do the same job in 12 hours. How long will it
take the two employees to finish the typing if they work together?
Make the chart below. It is just like a D=RT chart except that
D stands for "DEEDS" not "DISTANCE". In other words, D stands
for the number of DEEDS or typing jobs done in each case.
No of jobs Rate in jobs per hour Time in hours
Exec. sec.
Ord. employee
Both together
------------------------
We read:
>>...An executive secretary can finish a typing job in 10 hours...<<
So that's 1 job in 10 hours. So we fill in 1 for the number
of jobs which the executive secretary alone does and 10 for the number
of hours.
No of jobs Rate in jobs per hour Time in hours
Exec. sec. 1 10
Ord. employee
Both together
-------------
Next we read:
>>...an ordinary employee can do the same job in 12 hours...<<
That's 1 job in 12 hours. So we fill in 1 for the number
of jobs which the ordinary employee and 12 for the number of hours.
No of jobs Rate in jobs per hour Time in hours
Exec. sec. 1 10
Ord. employee 1 12
Both together
-----------------------
Now we read the question:
>>...How long will it take the two employees to finish the typing if they work together...<<
That asks how many hour would it take them both to do 1 job. So we
let x be the number of hours it would take them both to do 1 job. So
we fill in 1 for the number of jobs and x for the number of hours.
No of jobs Rate in jobs per hour Time in hours
Exec. sec. 1 10
Ord. employee 1 12
Both together 1 x
----------------------
Now we fill in the rates by using the equivalent of
DISTANCE
RATE = ----------
TIME
which is:
NUMBER of JOBS
RATE = -----------------
TIME
No of jobs Rate in jobs per hour Time in hours
Exec. sec. 1 1/10 10
Ord. employee 1 1/12 12
Both together 1 1/x x
Now we use the formula:
+ =
Can you solve that? You have to multiply through by the
LCD of 60x. If you can't solve it post again asking how.
Answer: hours.
Edwin