Two friends are painting a living room. Ken can paint it in 6 hours working alone. If Barbie works alone, it will take her 8 hours. How long will it take working together?

3 Answers
Mar 17, 2018

Let,the total work is of #x# amount.

So,ken does #x# amount of work in #6 hrs#

So,in #1 hr# he will do #x/6# amount of work.

Now,Barbie does #x# amount of work in #8 hrs#

So,in #1 hr# she does #x/8# amount of the work.

Let,after working #t hrs# together the work will be finished.

So, in #t hrs# Ken does #(xt)/6# amount of work and Barbie does #(xt)/8# amount of work.

Clearly, #(xt)/6 + (xt)/8 =x#

Or, #t/6 + t/8 =1#

So, #t=3.43 hrs#

Mar 17, 2018

Answer:

Detailed solution given so that you can see where everything comes from.

#3" hours and "25 5/7" minutes"larr" Exact value"#

#3" hours and "26" minutes"# to the nearest minute

Explanation:

People work at different rates. So the time taken by different people to complete a set amount of work will also be different. This is what we need to model

Let the total amount of work required to complete the task be #W#

Let Ken's work rate per hour be #w_k#
Let Barbie's work rate per hour be #w_b#
Let the total time working together be #t#

If Ken works on his own he can complete the whole task in 6 yours

#"work rate "xx" time = work done.".............Equation(1)#

#color(white)("ddd")w_kcolor(white)("dddd")xxcolor(white)("ddd")6color(white)("d")=color(white)("ddd")W#

So #w_k=W/6 ...........................Equation(2)#

If Barbie works on her own she can complete the whole task in 8 hours

Using the above method

#w_b=W/8........................Equation(3)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Consider #Eqn(1)# but combine the two work rates #Eqn(2)+Eqn(3)#

# color(white)("d") (w_bxxt) color(white)("d")+ color(white)("d")(w_kxxt)=W#

#(W/8xxt)+(W/6xxt)=W#

Factor out the #t#

#t(W/8+W/6)=W#

#t((3W)/24+(4W)/24)=W#

#t(7W)/24=W#

#t=(24cancel(W))/(7cancel(W))#

#t=24/7" hours"#

#t=3 3/7" hours"larr# Exact value

#t=3" hours and "(3/7xx60) #

#t= 3" hours and "25 5/7" minutes"larr" Exact value"#

Mar 17, 2018

Answer:

#3 3/7# hours or #3# hours and #26# minutes

Explanation:

First find out what fraction of the task they would each complete in #1# hour.

Ken will finish #1/6# of the task in #1# hour.

Barbie will finish #1/8# of the task in #1# hour.

If they work together, in one hour they will finish:

#1/6 +1/8# of the painting task.

#= (4+3)/24 = 7/24# is the fraction completed in one hour.

So to complete the whole task #(24/24)# we need to divide:

#24/24 div 7/24#

#=24/24 xx24/7#

#=24/7# hours.

This simplifies to #3 3/7# hours

Which is easier given as #3# hours and #3/7 xx60# minutes

#=3 " hours " and 25 5/7# minutes

or #3 " hours " and 26 # minutes