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Question 1166226: I have tried to solve this, and got an answer of "1.14 days".
But, I am a little bit confused...So, can you please help me with this.
Ana can finish her research project in 6 days and her parner can finish in 8 days, after working for three days, Ana's partner joined her, how long would it take to finish the project
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
the basic formula is r * t = q
r is the rate
t is the time
q is the quantity of work produced
when 2 people work together, their rates are additive.
the formula then becomes (r1 + r2) * t = q
when they work alone for the entire project, q becomes 1 because we have defined the quantity of work as completion of one project.
for ana, the formula becomes r * t = 1
for her partner, the formula becomes r * t = 1
since ana can complete the project in 6 days, her formula becomes r * 6 = 1.
solve for r to get r = 1/6.
this means ana can complete 1/6 of the job in 1 day.
since her partner can complete the project in 8 days, her formula becomes r * 8 = 1.
solve for r to get r = 1/8.
this means her partner can complete 1/8 of the job in 1 day.
you are given that ana worked alone for 3 days.
since she can complete 1/6 of the job in 1 day, then she can complete 3/6 of the job in 3 days.
r * t = q becomes 1/6 * 3 = q which becomes q = 1/2
ana has completed half of the job when her partner joins her.
they work together to complete the other half of the job.
they're working together, so (r1 + r2) * t = q becomes (1/6 + 1/8) * t = 1/2
q becomes 1/2 because 1/2 of the job remains to be done.
this becomes (1/6 + 1/8) * t = 1/2
a common denominator is 24, so the formula becomes:
(4/24 + 3/24) * t = 1/2
combine like terms to get 7/24 * t = 1/2
multiply both sides of this formula by 2 to get:
14/ * t = 1
solve for t to get:
t = 24/14 * 1 = 1 and 10/14 days.
this simplifies to 1 and 5/7 days.
place into decimal format and the answer is 1.714285714 days.
that should be your solution. ******************************************
add 3 days that ana worked on her own and the total time it took to finish the job ws 4.714285714 days.
your solution should be 1.714285714 days. ******************************
if you worked in decimal, then you should have gotten.
ana's rate is 1/6.
her partner's rate is 1/8.
in 3 hours ana completed 1/6 * 3 = 1/2 of the job = .5
when they worked together, (1/6 + 1/8) * t = .5
this becomes .29166666... * t = .5
solve for t to get t = .5 / .2916666..... = 1.714285714 days.
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